Problem Solving - HSPT Math
Card 1 of 8568
Helen wants to buy a dress for a party. It is on sale for 37% off. How much does the dress currently costs, if its original price was $45.00?
Helen wants to buy a dress for a party. It is on sale for 37% off. How much does the dress currently costs, if its original price was $45.00?
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First, multiply 45 by 0.37:
Then, subtract that amount from 45.00 to find the sale price:
Answer: The dress' sale price is $28.35.
First, multiply 45 by 0.37:
Then, subtract that amount from 45.00 to find the sale price:
Answer: The dress' sale price is $28.35.
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A restaurant is having a sale and lowering their prices by 20%. If an average meal for two normally costs $62.00, what will it costs under the current sale?
A restaurant is having a sale and lowering their prices by 20%. If an average meal for two normally costs $62.00, what will it costs under the current sale?
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Multiply: 
Then, subtract that amount from the original price:
Answer: $49.60
Multiply:
Then, subtract that amount from the original price:
Answer: $49.60
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If 
, then
can be rewritten as which of the following?
If
can be rewritten as which of the following?
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If 
, then
, so
.
Also,
, so
Therefore,
If
Also,
Therefore,
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What is 
?
What is
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Divide both sides by 13:
Divide both sides by 13:
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What is s?
What is s?
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Divide both sides by 4:
Divide both sides by 4:
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First, divide by 36 on each side:
First, divide by 36 on each side:
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What is 
?
What is
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Divide both sides by 11:
Divide both sides by 11:
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A metal cylindrical brick has a height of 
. The area of the top is 
. A circular hole with a radius of 
is centered and drilled half-way down the brick. What is the volume of the resulting shape?
A metal cylindrical brick has a height of
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To find the final volume, we will need to subtract the volume of the hole from the total initial volume of the cylinder.
The volume of a cylinder is given by the product of the base area times the height: 
.
Find the initial volume using the given base area and height.
Next, find the volume of the hole that was drilled. The base area of this cylinder can be calculated from the radius of the hole. Remember that the height of the hole is only half the height of the block.
Finally, subtract the volume of the hole from the total initial volume.
To find the final volume, we will need to subtract the volume of the hole from the total initial volume of the cylinder.
The volume of a cylinder is given by the product of the base area times the height:
Find the initial volume using the given base area and height.
Next, find the volume of the hole that was drilled. The base area of this cylinder can be calculated from the radius of the hole. Remember that the height of the hole is only half the height of the block.
Finally, subtract the volume of the hole from the total initial volume.
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If a waterproof box is 50cm in length, 20cm in depth, and 30cm in height, how much water will overflow if 35 liters of water are poured into the box?
If a waterproof box is 50cm in length, 20cm in depth, and 30cm in height, how much water will overflow if 35 liters of water are poured into the box?
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The volume of the box is 50 * 20 * 30 cm = 30,000 cm3.
1cm3 = 1mL, 30,000 cm3 = 30,000mL = 30 L.
Because the volume of the box is only 30 L, 5 L of the 35 L will not fit into the box.
The volume of the box is 50 * 20 * 30 cm = 30,000 cm3.
1cm3 = 1mL, 30,000 cm3 = 30,000mL = 30 L.
Because the volume of the box is only 30 L, 5 L of the 35 L will not fit into the box.
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What is 
decreased by 40%?
What is
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Decreasing a number by 40% is equivalent to taking 60% of a number, which in turn is equivalent to multiplying it by
.
decreased by 40% is the product of 
and 
:
, so the correct response is 
.
Decreasing a number by 40% is equivalent to taking 60% of a number, which in turn is equivalent to multiplying it by
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What is 
?
What is
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First, subtract 14 from each side:
Then, divide each side by 8:
First, subtract 14 from each side:
Then, divide each side by 8:
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A rectangular prism has a length that is twice as long as its width, and a width that is twice as long as its height. If the surface area of the prism is 252 square units, what is the volume, in cubic units, of the prism?
A rectangular prism has a length that is twice as long as its width, and a width that is twice as long as its height. If the surface area of the prism is 252 square units, what is the volume, in cubic units, of the prism?
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Let l be the length, w be the width, and h be the height of the prism. We are told that the length is twice the width, and that the width is twice the height. We can set up the following two equations:
l = 2_w_
w = 2_h_
Next, we are told that the surface area is equal to 252 square units. Using the formula for the surface area of the rectangular prism, we can write the following equation:
surface area = 2_lw_ + 2_lh_ + 2_wh_ = 252
We now have three equations and three unknowns. In order to solve for one of the variables, let's try to write w and l in terms of h. We know that w = 2_h_. Because l = 2_w_, we can write l as follows:
l = 2_w_ = 2(2_h_) = 4_h_
Now, let's substitute w = 2_h_ and l = 4_h_ into the equation we wrote for surface area.
2(4_h_)(2_h_) + 2(4_h_)(h) + 2(2_h_)(h) = 252
Simplify each term.
16_h_2 + 8_h_2 + 4_h_2 = 252
Combine _h_2 terms.
28_h_2 = 252
Divide both sides by 28.
_h_2 = 9
Take the square root of both sides.
h = 3.
This means that h = 3. Because w = 2_h_, the width must be 6. And because l = 2_w_, the length must be 12.
Because we now know the length, width, and height, we can find the volume of the prism, which is what the question ultimately requires us to find.
volume of a prism = l • w • h
volume = 12(6)(3)
= 216 cubic units
The answer is 216.
Let l be the length, w be the width, and h be the height of the prism. We are told that the length is twice the width, and that the width is twice the height. We can set up the following two equations:
l = 2_w_
w = 2_h_
Next, we are told that the surface area is equal to 252 square units. Using the formula for the surface area of the rectangular prism, we can write the following equation:
surface area = 2_lw_ + 2_lh_ + 2_wh_ = 252
We now have three equations and three unknowns. In order to solve for one of the variables, let's try to write w and l in terms of h. We know that w = 2_h_. Because l = 2_w_, we can write l as follows:
l = 2_w_ = 2(2_h_) = 4_h_
Now, let's substitute w = 2_h_ and l = 4_h_ into the equation we wrote for surface area.
2(4_h_)(2_h_) + 2(4_h_)(h) + 2(2_h_)(h) = 252
Simplify each term.
16_h_2 + 8_h_2 + 4_h_2 = 252
Combine _h_2 terms.
28_h_2 = 252
Divide both sides by 28.
_h_2 = 9
Take the square root of both sides.
h = 3.
This means that h = 3. Because w = 2_h_, the width must be 6. And because l = 2_w_, the length must be 12.
Because we now know the length, width, and height, we can find the volume of the prism, which is what the question ultimately requires us to find.
volume of a prism = l • w • h
volume = 12(6)(3)
= 216 cubic units
The answer is 216.
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A foam ball has a volume of 2 units and has a diameter of x. If a second foam ball has a radius of 2x, what is its volume?
A foam ball has a volume of 2 units and has a diameter of x. If a second foam ball has a radius of 2x, what is its volume?
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Careful not to mix up radius and diameter. First, we need to identify that the second ball has a radius that is 4 times as large as the first ball. The radius of the first ball is (1/2)x and the radius of the second ball is 2x. The volume of the second ball will be 43, or 64 times bigger than the first ball. So the second ball has a volume of 2 * 64 = 128.
Careful not to mix up radius and diameter. First, we need to identify that the second ball has a radius that is 4 times as large as the first ball. The radius of the first ball is (1/2)x and the radius of the second ball is 2x. The volume of the second ball will be 43, or 64 times bigger than the first ball. So the second ball has a volume of 2 * 64 = 128.
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Kim from Idaho can only stack bales of hay in her barn for 3 hours before she needs a break. She stacks the bales at a rate of 2 bales per minute, 3 bales high with 5 bales in a single row. How many full rows will she have at the end of her stacking?
Kim from Idaho can only stack bales of hay in her barn for 3 hours before she needs a break. She stacks the bales at a rate of 2 bales per minute, 3 bales high with 5 bales in a single row. How many full rows will she have at the end of her stacking?
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She will stack 360 bales in 3 hours. One row requires 15 bales. 360 divided by 15 is 24.
She will stack 360 bales in 3 hours. One row requires 15 bales. 360 divided by 15 is 24.
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What is the volume of a right cylinder with a circumference of 25π in and a height of 41.3 in?
What is the volume of a right cylinder with a circumference of 25π in and a height of 41.3 in?
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The formula for the volume of a right cylinder is: V = A * h, where A is the area of the base, or πr2. Therefore, the total formula for the volume of the cylinder is: V = πr2h.
First, we must solve for r by using the formula for a circumference (c = 2πr): 25π = 2πr; r = 12.5.
Based on this, we know that the volume of our cylinder must be: π*12.52*41.3 = 6453.125π in3
The formula for the volume of a right cylinder is: V = A * h, where A is the area of the base, or πr2. Therefore, the total formula for the volume of the cylinder is: V = πr2h.
First, we must solve for r by using the formula for a circumference (c = 2πr): 25π = 2πr; r = 12.5.
Based on this, we know that the volume of our cylinder must be: π*12.52*41.3 = 6453.125π in3
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What is the volume of a cylinder with a diameter of 13 inches and a height of 27.5 inches?
What is the volume of a cylinder with a diameter of 13 inches and a height of 27.5 inches?
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The equation for the volume of a cylinder is V = Ah, where A is the area of the base and h is the height.
Thus, the volume can also be expressed as V = πr2h.
The diameter is 13 inches, so the radius is 13/2 = 6.5 inches.
Now we can easily calculate the volume:
V = 6.52π * 27.5 = 1161.88π in3
The equation for the volume of a cylinder is V = Ah, where A is the area of the base and h is the height.
Thus, the volume can also be expressed as V = πr2h.
The diameter is 13 inches, so the radius is 13/2 = 6.5 inches.
Now we can easily calculate the volume:
V = 6.52π * 27.5 = 1161.88π in3
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An 8-inch cube has a cylinder drilled out of it. The cylinder has a radius of 2.5 inches. To the nearest hundredth, approximately what is the remaining volume of the cube?
An 8-inch cube has a cylinder drilled out of it. The cylinder has a radius of 2.5 inches. To the nearest hundredth, approximately what is the remaining volume of the cube?
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We must calculate our two volumes and subtract them. The volume of the cube is very simple: 8 * 8 * 8, or 512 in3.
The volume of the cylinder is calculated by multiplying the area of its base by its height. The height of the cylinder is 8 inches (the height of the cube through which it is being drilled). Therefore, its volume is πr2h = π * 2.52 * 8 = 50π in3
The volume remaining in the cube after the drilling is: 512 – 50π, or approximately 512 – 157.0795 = 354.9205, or 354.92 in3.
We must calculate our two volumes and subtract them. The volume of the cube is very simple: 8 * 8 * 8, or 512 in3.
The volume of the cylinder is calculated by multiplying the area of its base by its height. The height of the cylinder is 8 inches (the height of the cube through which it is being drilled). Therefore, its volume is πr2h = π * 2.52 * 8 = 50π in3
The volume remaining in the cube after the drilling is: 512 – 50π, or approximately 512 – 157.0795 = 354.9205, or 354.92 in3.
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An 12-inch cube of wood has a cylinder drilled out of it. The cylinder has a radius of 3.75 inches. If the density of the wood is 4 g/in3, what is the mass of the remaining wood after the cylinder is drilled out?
An 12-inch cube of wood has a cylinder drilled out of it. The cylinder has a radius of 3.75 inches. If the density of the wood is 4 g/in3, what is the mass of the remaining wood after the cylinder is drilled out?
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We must calculate our two volumes and subtract them. Following this, we will multiply by the density.
The volume of the cube is very simple: 12 * 12 * 12, or 1728 in3.
The volume of the cylinder is calculated by multiplying the area of its base by its height. The height of the cylinder is 8 inches (the height of the cube through which it is being drilled). Therefore, its volume is πr2h = π * 3.752 * 12 = 168.75π in3.
The volume remaining in the cube after the drilling is: 1728 – 168.75π, or approximately 1728 – 530.1433125 = 1197.8566875 in3. Now, multiply this by 4 to get the mass: (approx.) 4791.43 g.
We must calculate our two volumes and subtract them. Following this, we will multiply by the density.
The volume of the cube is very simple: 12 * 12 * 12, or 1728 in3.
The volume of the cylinder is calculated by multiplying the area of its base by its height. The height of the cylinder is 8 inches (the height of the cube through which it is being drilled). Therefore, its volume is πr2h = π * 3.752 * 12 = 168.75π in3.
The volume remaining in the cube after the drilling is: 1728 – 168.75π, or approximately 1728 – 530.1433125 = 1197.8566875 in3. Now, multiply this by 4 to get the mass: (approx.) 4791.43 g.
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First, subtract 
from each side:
Then, divide each side by 
:
First, subtract
Then, divide each side by
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Diveide each side by 
:
Diveide each side by
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