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SAT Math : Algebraic Fractions

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Example Question #61 : Algebraic Fractions

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?

Possible Answers:

2100sc

300c/s

21sc/100

2100s/c

3c/(100s)

Correct answer:

21sc/100

Explanation:

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.

Sweaters

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Example Question #3 : How To Solve For A Variable As Part Of A Fraction

If $\dpi{100} \small z>0$ , what is 40 percent of $\dpi{100} \small 30z$ ?

Possible Answers:

$\dpi{100} \small 120z$

$\dpi{100} \small 30z$

$\dpi{100} \small 20z$

$\dpi{100} \small 5z$

$\dpi{100} \small 12z$

Correct answer:

$\dpi{100} \small 12z$

Explanation:

To find 40 percent of $\dpi{100} \small 30z$ multiply $\dpi{100} \small 30z\times 0.4$

The result is $\dpi{100} \small 12z$

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Example Question #4 : How To Solve For A Variable As Part Of A Fraction

Solve for .

$\frac{1}{3}(3x-6)+\frac{1}{2}(2x+4)=\frac{1}{5}(15x -5)$

Possible Answers:

$-3$

$2$

$0$

$-2$

Correct answer:

Explanation:

First distribute the fractions:

x-2 +x+2 =3x-1

Combine like terms:

2x=3x-1

x=1

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Example Question #5 : How To Solve For A Variable As Part Of A Fraction

Solve for $x$ .

$(2x+3)-3(x+5)=-(3x-4)$

Possible Answers:

$4$

$0$

$-8$

$-4$

Correct answer:

Explanation:

First distribute to eliminate the parentheses:

$2x+3-3x-15=-3x+4$

Then combine like terms:

$2x=16$

$x=8$

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Example Question #1 : How To Solve For A Variable As Part Of A Fraction

x = 1/2

What does 1/x + 1/(x + 4) equal?

Possible Answers:

20/9

4/9

9/2

Correct answer:

20/9

Explanation:

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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Example Question #1 : How To Solve For A Variable As Part Of A Fraction

Solve for .

$\frac{16}{x + 7} = \frac{2}{6}$

Possible Answers:

Correct answer:

Explanation:

Cross multiply. 96 = 2 (x+7)

Dsitribute. 96 = 2x + 14

Solve for . 96 - 14 = 2x

82 = 2x

41 = x

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Example Question #6 : How To Solve For A Variable As Part Of A Fraction

If x=-5 , what is the value of $\frac{x^{2}+20}{x-4}$ ?

Possible Answers:

Correct answer:

Explanation:

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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Example Question #1151 : Algebra

Solve:

$\frac{4}{11}x + 3 = 15$

Possible Answers:

x = 37

x = 29

$x = \frac{48}{11}$

x = 39

x = 33

Correct answer:

x = 33

Explanation:

We want to isolate the x. First, we take away 3 from both sides. Then we have:

$\frac{4}{11}x = 12$

To get x by itself, we multiply by the reciprocal on both sides.

Then, we have:

$x = 12 \times \frac{11}{4} = \frac{12}{1}\times\frac{11}{4} = \frac{132}{4} = 33$

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Example Question #3241 : Sat Mathematics

If $\frac{6}{x}=\frac{9}{19}$ , then what is the value of ?

Possible Answers:

none of these

3/38

9/114

38/3

7/12

Correct answer:

38/3

Explanation:

cross multiply:

(6)(19) = 9x

114=9x

x = 38/3

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Example Question #1 : How To Solve For A Variable As Part Of A Fraction

$\dpi{100} \small \frac{4 }{x} = \frac{2}{25}$

Find x.

Possible Answers:

$\dpi{100} \small \frac{8}{25}$

$\dpi{100} \small 0.25$

$\dpi{100} \small 50$

None

$\dpi{100} \small \frac{25}{8}$

Correct answer:

$\dpi{100} \small 50$

Explanation:

Cross multiply:

$\dpi{100} \small 4 \times 25 = 2x$

$\dpi{100} \small 100 = 2x$

$\dpi{100} \small x = 50$

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SAT Math : Algebraic Fractions

Study concepts, example questions & explanations for SAT Math

All SAT Math Resources

Example Questions

Example Question #61 : Algebraic Fractions

Example Question #3 : How To Solve For A Variable As Part Of A Fraction

Example Question #4 : How To Solve For A Variable As Part Of A Fraction

Example Question #5 : How To Solve For A Variable As Part Of A Fraction

Example Question #1 : How To Solve For A Variable As Part Of A Fraction

Example Question #1 : How To Solve For A Variable As Part Of A Fraction

Example Question #6 : How To Solve For A Variable As Part Of A Fraction

Example Question #1151 : Algebra

Example Question #3241 : Sat Mathematics

Example Question #1 : How To Solve For A Variable As Part Of A Fraction

All SAT Math Resources

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