How to solve one-step equations - HSPT Math

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Question

Suzanne is at the grocery store. She has $5.00 to spend on produce. Oranges are $2.50 per pound, apples cost $1.50 per pound and bananas are $0.50 per pound. Which combination of fruit will fit her budget?

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Answer

Make a simple algebra equation and test it against each combination:

Total Cost = $2.50 * (# Oranges) + $1.50 * (# Apples) + $0.50 * (# Bananas)

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Question

Solve for : $A = \frac{5k}{7y}$

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Answer

$A = \frac{5k}{7y}$

$A \cdot \frac{7y}{5} = \frac{5k}{7y} \cdot \frac{7y}{5}$

$\frac{A}{1} \cdot \frac{7y}{5} = k$

$k= \frac{7Ay}{5}$

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Question

Ann, Bailey, Cara, Jack, and Jill are running a marathon. Cara finishes 4 minutes before Ann. Jill finishes after Bailey, who finishes after Ann. Jack finishes right before Bailey. Who else does Jack finish the race before?

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Answer

Cara finishes first. Ann and Bailey finish before Jill. If Jack finishes right before Bailey, then Jill finishes last.

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Question

Jasmine is participating in a swimming race. If the race is 3000 yards, what percentage of the race has she completed at the 2400 yardline?

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Answer

Divide $2400\div 3000=.80$ .

Answer: Jasmine has completed 80% of the race.

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Question

A full helium tank can blow up 50 balloons. At least how many times does the tank have to be re-filled in order to blow up 140 balloons?

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Answer

Divide $140\div 50=2.8$

Answer: The tank must be filled up at least 3 times.

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Question

Alegra is taking a cooking class with friends. It is 40 dollars for every two people who participate because people are supposed to work in pairs. But if someone does not have a partner, that person can still participate but must pay $30 for him or herself. Alegra's four best friends participate in the class with her, and they divide the cost evenly. What is the total cost per person?

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Answer

Since Alegra is taking the class with 4 friends, that means there are a total of 5 people. This means that there are 2 pairs of friends, and one alone friend.

Below are the prices that will be charged based on this make up:

2 pairs of people at 40 dollars per pair = 80 dollars

1 solo person at 30 dollars per person = 30 dollars

80 dollars plus 30 dollars is 110 dollars, the grand total.

When 110 dollars is divided by 5, the answer is 22. Therefore, 22 dollars is the correct answer.

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Question

In a math contest, the team from Lincoln High comprised five students - Melanie, Ned, Olivia, Phyllis, and Quinn. Melanie outscored Ned by 12 points; Ned outscored Quinn by 19 points; Phyllis outscored Ned by 45 points and Olivia by 20 points. Who came in third among the five?

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Answer

Since this reasoning is valid regardless of the actual scores, suppose Quinn scored 100. Then Ned scored 19 more than Quinn, or 119, and Melanie scored 12 more than Ned, or 131. Phyllis scored 45 more than Ned, or 164, and Olivia scored 20 points fewer than Phyllis, or 144. This makes the order, from greatest to least:

Phyllis, Olivia, Melanie, Ned, Quinn

Melanie scored third among the five.

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Question

Solve:

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Answer

To solve for , divide by eight on both sides of the equation.

$\frac{8x}{8}=\frac{3200}{8}$

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Question

Solve for : $-\frac{y}{3} = 2$

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Answer

To isolate the unknown variable, multiply both sides by negative three.

$-\frac{y}{3} \times -3= 2 \times -3$

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Question

Solve: $\frac{x}{0.02} = 50$

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Answer

Multiply on both sides of the equation to isolate the variable.

$\frac{x}{0.02} \times 0.02= 50\times 0.02$

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Question

Solve: $4x = \frac{1}{8}$

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Answer

To isolate the unknown variable, multiply both sides by one-fourth.

$4x \times (\frac{1}{4})= \frac{1}{8}\times (\frac{1}{4})$

$x=\frac{1}{32}$

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Question

Solve for :

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Answer

In order to solve this equation we need to isolate the variable to one side. Do not forget to perform the same operation on both sides of the equation.

Subtract from both sides of the equation.

Solve.

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Question

If , solve for .

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Answer

First, subtract 3 from both sides:

$\dpi{100} 4x+3-3=15-3$

$\dpi{100} 4x=12$

Now divide by 4 on both sides:

$\dpi{100} \frac{4x}{4}=\frac{12}{4}$

$\dpi{100} x=3$

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Question

$3a+8+7=14\times 3=$

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Answer

To solve:

First, solve both equations on each end, keeping the variable.

$\small 3a+ 8+ 7 = 14\cdot 3$

Then, subtract 15 from each side of the equation.

Finally, divide each side by 3 so that only the variable remains.

$\small 3a\div 3=27\div 3$

$\small \small a=9$

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Question

Solve for :

$\frac{3}{4} t = \frac{4}{3}$

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Answer

Divide both sides by $\frac{3}{4}$ :

$\frac{3}{4} t = \frac{4}{3}$

$\frac{3}{4} t \div \frac{3}{4}= \frac{4}{3} \div \frac{3}{4}$

$t = \frac{4}{3} \cdot \frac{4}{3} = \frac{4\cdot 4}{3\cdot 3} = \frac{16}{9}$

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Question

Solve for :

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Answer

Subtract 19, then divide by 7:

$7n \div 7= 63 \div 7$

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Question

A bicycle originally costs $120.00. If it is on sale for 30% off, what is the sale price of the bicycle?

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Answer

First multiply the original price by 30%.

$120\ast .30=36$

Then subtract that amount from the original price.

The sale price is $84.00

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Question

$8\cdot \left ( 2\cdot 5 \right ) \div \left ( 4\cdot 1 \right )=$

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Answer

First solve the parentheses.

$8 * 10 \div 4=$

Then solve from left to right since multiplication and division are interchangeable:

$80\div 4=20$

The answer is 20.

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Question

$3 \frac{2}{6} \ast 2\frac{3}{4}=$

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Answer

First, convert each mixed number into an improper fraction.

$\frac{20}{6}\ast \frac{11}{4}$

Then, reduce where possible and multiply.

Finally, convert your answer into a mixed-number fraction.

$\frac{55}{6}=9 {\frac{1}{6}}$

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Question

$11 \frac{1}{4} \div 5\frac{2}{5}=$

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Answer

First, convert each mixed number into an improper fraction and flip the second fraction. Then, change the operation to multiplication:

$\frac{45}{4} \ast \frac{5}{27}=$

Reduce where possible and multiply. Convert your answer into a mixed fraction.

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