How to solve for a variable as part of a fraction - PSAT Math
Card 1 of 98
If 
, what is the value of 
?
If
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To solve this question, substitute -5 in for x in the numerator and denominator. Remember that the square of a negative number is positive.
45 / -9 = -5
To solve this question, substitute -5 in for x in the numerator and denominator. Remember that the square of a negative number is positive.
45 / -9 = -5
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If (t-5)/2t =13/19, what is the value of t?
If (t-5)/2t =13/19, what is the value of t?
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We start by cross multiplying to get the equation 26t=19t-95. We then subtract 19t from 26t giving us 7t= -95. We then divide by 7, giving us t= (-95)/7.
We start by cross multiplying to get the equation 26t=19t-95. We then subtract 19t from 26t giving us 7t= -95. We then divide by 7, giving us t= (-95)/7.
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x = 1/2
What does 1/x + 1/(x + 4) equal?
x = 1/2
What does 1/x + 1/(x + 4) equal?
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1/x + 1/(x+4) =
1/(1/2) + 1/ (1/2 + 4) =
1/ (1/2) + 1 / (9/2) =
2 + 2/9
20/9
1/x + 1/(x+4) =
1/(1/2) + 1/ (1/2 + 4) =
1/ (1/2) + 1 / (9/2) =
2 + 2/9
20/9
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If 
, then what is the value of 
?
If 
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cross multiply:
(6)(19) = 9x
114=9x
x = 38/3
cross multiply:
(6)(19) = 9x
114=9x
x = 38/3
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If x/3 = 50, then what is x/10 equal to?
If x/3 = 50, then what is x/10 equal to?
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1. Solve for x in x/3 = 50
2. x = 150
3.Substitute 150 for x in x/10
4. x = 15
1. Solve for x in x/3 = 50
2. x = 150
3.Substitute 150 for x in x/10
4. x = 15
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The numerator of a fraction is the sum of 4 and 5 times the denominator. If you divide the fraction by 2, the numerator is 3 times the denominator. Find the simplified version of the fraction.
The numerator of a fraction is the sum of 4 and 5 times the denominator. If you divide the fraction by 2, the numerator is 3 times the denominator. Find the simplified version of the fraction.
Tap to reveal answer
Let numerator = N and denominator = D.
According to the first statement,
N = (D x 5) + 4.
According to the second statement, N / 2 = 3 * D.
Let's multiply the second equation by –2 and add itthe first equation:
–N = –6D
+\[N = (D x 5) + 4\]
=
–6D + (D x 5) + 4 = 0
–1D + 4 = 0
D = 4
Thus, N = 24.
Therefore, N/D = 24/4 = 6.
Let numerator = N and denominator = D.
According to the first statement,
N = (D x 5) + 4.
According to the second statement, N / 2 = 3 * D.
Let's multiply the second equation by –2 and add itthe first equation:
–N = –6D
+\[N = (D x 5) + 4\]
=
–6D + (D x 5) + 4 = 0
–1D + 4 = 0
D = 4
Thus, N = 24.
Therefore, N/D = 24/4 = 6.
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The maximum number of sweaters that Lauren can sew every day is equal to s, and the amount, in cents, that she charges for each sweater is equal to c. Which of the following expressions is equivalent to the maximum amount of money that Lauren can make, in dollars, after three weeks?
The maximum number of sweaters that Lauren can sew every day is equal to s, and the amount, in cents, that she charges for each sweater is equal to c. Which of the following expressions is equivalent to the maximum amount of money that Lauren can make, in dollars, after three weeks?
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The amount of money that Lauren can make depends on the number of sweaters that she can make. If she makes at most s sweaters a day, then we can multiply the number of days that she works by s to determine the total number of sweaters she makes.
total number of sweaters = (s)(number of days)
We are told to consider a time interval of three weeks. Because there are seven days in one week, the number of days over this period of time would equal 3(7), or 21 days. In other words, there are 21 days in three weeks Thus, the number of sweaters is equal to the product of s and 21.
total number of sweaters = (s)(21)
Now that we have the number of sweaters Lauren can make, we can multiply this by the cost of each sweater, which is equal to c cents, in order to obtain the amount of money she eared.
amount of money earned = (number of sweaters)(cost of each sweater)
amount of money earned = s(21)(c)
However, because the price of each sweater is given in terms of cents, the amount of money s(21)(c) will be equal to the number of cents she makes. The question, though, asks us to find the amount of money in dollars. We must use a conversion factor to change the number of cents to dollars. Remember that there are 100 cents per dollar.
The amount of money that Lauren can make depends on the number of sweaters that she can make. If she makes at most s sweaters a day, then we can multiply the number of days that she works by s to determine the total number of sweaters she makes.
total number of sweaters = (s)(number of days)
We are told to consider a time interval of three weeks. Because there are seven days in one week, the number of days over this period of time would equal 3(7), or 21 days. In other words, there are 21 days in three weeks Thus, the number of sweaters is equal to the product of s and 21.
total number of sweaters = (s)(21)
Now that we have the number of sweaters Lauren can make, we can multiply this by the cost of each sweater, which is equal to c cents, in order to obtain the amount of money she eared.
amount of money earned = (number of sweaters)(cost of each sweater)
amount of money earned = s(21)(c)
However, because the price of each sweater is given in terms of cents, the amount of money s(21)(c) will be equal to the number of cents she makes. The question, though, asks us to find the amount of money in dollars. We must use a conversion factor to change the number of cents to dollars. Remember that there are 100 cents per dollar.
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Find x.
Find x.
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Cross multiply:
Cross multiply:
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If 
, what is 40 percent of 
?
If
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To find 40 percent of 
multiply 
The result is 
To find 40 percent of
The result is
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Solve for 
.
Solve for
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First distribute the fractions:
Combine like terms:
First distribute the fractions:
Combine like terms:
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Solve for 
.
Solve for
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First distribute to eliminate the parentheses:
Then combine like terms:
First distribute to eliminate the parentheses:
Then combine like terms:
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There are m number of people on a deserted island. They drink n liters of water a day. There are x number of 10 liter bottles on the island. On what day will they run out of water?
There are m number of people on a deserted island. They drink n liters of water a day. There are x number of 10 liter bottles on the island. On what day will they run out of water?
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There are only x * 10 liters of water on the island. n * m equals how many liters are consumed per day. Divide x * 10 liters by n * m. Note the units (days) are correct in the answer.
There are only x * 10 liters of water on the island. n * m equals how many liters are consumed per day. Divide x * 10 liters by n * m. Note the units (days) are correct in the answer.
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Solve for 
.
Solve for
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Cross multiply. 
Dsitribute. 
Solve for 
. 
Cross multiply.
Dsitribute.
Solve for
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Solve for 
:
Solve for
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Solve for 
:
Step 1: Cross-multiply to eliminate the fraction
Step 2: Solve for 
:
Solve for
Step 1: Cross-multiply to eliminate the fraction
Step 2: Solve for
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If , then what is the value of ?
If
Tap to reveal answer
cross multiply:
(6)(19) = 9x
114=9x
x = 38/3
cross multiply:
(6)(19) = 9x
114=9x
x = 38/3
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If x/3 = 50, then what is x/10 equal to?
If x/3 = 50, then what is x/10 equal to?
Tap to reveal answer
1. Solve for x in x/3 = 50
2. x = 150
3.Substitute 150 for x in x/10
4. x = 15
1. Solve for x in x/3 = 50
2. x = 150
3.Substitute 150 for x in x/10
4. x = 15
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If , what is the value of ?
If
Tap to reveal answer
To solve this question, substitute -5 in for x in the numerator and denominator. Remember that the square of a negative number is positive.
45 / -9 = -5
To solve this question, substitute -5 in for x in the numerator and denominator. Remember that the square of a negative number is positive.
45 / -9 = -5
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If (t-5)/2t =13/19, what is the value of t?
If (t-5)/2t =13/19, what is the value of t?
Tap to reveal answer
We start by cross multiplying to get the equation 26t=19t-95. We then subtract 19t from 26t giving us 7t= -95. We then divide by 7, giving us t= (-95)/7.
We start by cross multiplying to get the equation 26t=19t-95. We then subtract 19t from 26t giving us 7t= -95. We then divide by 7, giving us t= (-95)/7.
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x = 1/2
What does 1/x + 1/(x + 4) equal?
x = 1/2
What does 1/x + 1/(x + 4) equal?
Tap to reveal answer
1/x + 1/(x+4) =
1/(1/2) + 1/ (1/2 + 4) =
1/ (1/2) + 1 / (9/2) =
2 + 2/9
20/9
1/x + 1/(x+4) =
1/(1/2) + 1/ (1/2 + 4) =
1/ (1/2) + 1 / (9/2) =
2 + 2/9
20/9
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The numerator of a fraction is the sum of 4 and 5 times the denominator. If you divide the fraction by 2, the numerator is 3 times the denominator. Find the simplified version of the fraction.
The numerator of a fraction is the sum of 4 and 5 times the denominator. If you divide the fraction by 2, the numerator is 3 times the denominator. Find the simplified version of the fraction.
Tap to reveal answer
Let numerator = N and denominator = D.
According to the first statement,
N = (D x 5) + 4.
According to the second statement, N / 2 = 3 * D.
Let's multiply the second equation by –2 and add itthe first equation:
–N = –6D
+\[N = (D x 5) + 4\]
=
–6D + (D x 5) + 4 = 0
–1D + 4 = 0
D = 4
Thus, N = 24.
Therefore, N/D = 24/4 = 6.
Let numerator = N and denominator = D.
According to the first statement,
N = (D x 5) + 4.
According to the second statement, N / 2 = 3 * D.
Let's multiply the second equation by –2 and add itthe first equation:
–N = –6D
+\[N = (D x 5) + 4\]
=
–6D + (D x 5) + 4 = 0
–1D + 4 = 0
D = 4
Thus, N = 24.
Therefore, N/D = 24/4 = 6.
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