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SAT Math : Linear / Rational / Variable Equations

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Example Questions

Example Question #31 : Linear / Rational / Variable Equations

If $\$$ is defined for all numbers and to be $x\$y$ $x^2 - 2xy$ , then what is $4\$2$ ?

Possible Answers:

Correct answer:

Explanation:

In evaluating, we can simply plug in 4 and 2 for and respectively. We then get 16-16=0 .

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Example Question #71 : How To Find The Solution To An Equation

Internet service costs $0.50 per minute for the first ten minutes and is $0.20 a minute thereafter. What is the equation that represents the cost of internet in dollars when time is greater than 10 minutes?

Possible Answers:

5.00 + 0.20 (x-10)

5 + 0.20 (x+10)

5.00

5.00 + 0.20 (x)

10 + 0.20 (x-10)

Correct answer:

5.00 + 0.20 (x-10)

Explanation:

The first ten minutes will cost $5. From there we need to apply a $0.20 per-minute charge for every minute after ten. This gives

$\$0.20(x-10)+5$ .

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Example Question #32 : Algebra

John goes on a trip of kilometers at a speed of kilometers an hour. How long did the trip take?

Possible Answers:

c/b

b-c

c-b

c+b

b/c

Correct answer:

b/c

Explanation:

If we take the units and look at division, miles/(miles/hour) will yield hours as a unit. Therefore the answer is b/c .

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Example Question #33 : Algebra

With a $25\ mph$ head wind a plane can fly a certain distance in five hours. The return flight takes an hour less. How fast was the plane flying?

Possible Answers:

$300\ mph$

$225\ mph$

$275\ mph$

$175\ mph$

$125\ mph$

Correct answer:

$225\ mph$

Explanation:

In general, $distance=rate\times time$ .

The distance is the same going and coming; however, the head wind affects the rate. The equation thus becomes $(r-25)\times 5=(r+25)\times 4$ .

Solving for $r$ gives $r=225\ mph$ .

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Example Question #71 : How To Find The Solution To An Equation

How much water should be added to $2\ L$ of 90% cleaning solution to yield 50% cleaning solution?

Possible Answers:

$2.4\ L$

$0.8\ L$

$1.6\ L$

$1.2\ L$

$1.5\ L$

Correct answer:

$1.6\ L$

Explanation:

Pure water is 0% and pure solution 100%. Let $x$ = water to be added.

$V_{1}P_{1} + V_{2}P_{2} = V_{f}P_{f}$ in general where $V$ is the volume and $P$ is the percent.

So the equation to solve becomes $x(0)+2(0.90)= (x+2)(0.50)$

and $x=1.6\ L$

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Example Question #31 : Linear / Rational / Variable Equations

Solve $x+2y=14$ and $2x+y=13$

Possible Answers:

$(4,5)$

$(1,3)$

$(-4,-5)$

$(5,4)$

$(3,2)$

Correct answer:

$(4,5)$

Explanation:

This problem is a good example of the substitution method of solving a system of equations. We start by rewritting the first equation in terms of $x$ to get $x=14-2y$ and then substutite the $x$ into the second equation to get

$2(14-2y)+y=13$ .

Solving this equation gives $y=5$ and substituting this value into one of the original equations gives $x=4$ , thus the correct answer is $(4,5)$ .

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Example Question #43 : Linear / Rational / Variable Equations

Joy bought some art supplies. She bought colored pencils for $1.25 per box and sketch pads for $2.25 each. Joy bought one more sketch pad than colored pencil boxes and spent $9.25. How many sketch pads did she buy?

Possible Answers:

$2$

$4$

$3$

$5$

$1$

Correct answer:

$3$

Explanation:

Let $x$ = # of color pencil boxes and $x+1$ = # of sketch pads purchased.

So the equation to solve becomes $1.25x+2.25(x+1)=9.25$ .

Solving this equations leads to 2 colored pencil boxes and 3 sketch pads.

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Example Question #35 : Algebra

$\left | 2x - 3 \right |-x= 5$

Possible Answers:

$x=-8\ or \ x=-\frac{3}{2}$

$x=-8$

$x=-\frac{2}{3}$

$x=8\ or\ x=-\frac{2}{3}$

$x=8$

Correct answer:

$x=8\ or\ x=-\frac{2}{3}$

Explanation:

This question deals with absolute value equations which will normally gives you two solutions.

You need to solve two sets of equations for absolute value problems:

$2x-3 = x+5$

and

$2x-3=-\left ( x+5 \right )$

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Example Question #1811 : Sat Mathematics

Steve sells cars. His monthly salary is $1,000. He gets a $500 commission for each car he sells. If Steve wants to make $7,500 this month, how many cars would he have to sell?

Possible Answers:

Correct answer:

Explanation:

Let = money earned and = number of cars sold

So y = 500x + 1000

7500 = 500x + 1000 and solving shows that he needs to sell 13 cars to make $7,500.

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Example Question #37 : Algebra

A chemistry student needs to dilute some acid. How much pure water should be added to 2 gallons of 80% acid solution to yield 20% acid solution?

Possible Answers:

$5\ gallons$

$4\ gallons$

$8\ gallons$

$6\ gallons$

$2\ gallons$

Correct answer:

$6\ gallons$

Explanation:

Let pure water = 0 % and pure acid = 100%

The general equation to use is:

$V_{1}P_{1} + V_{2}P_{2} = V_{f}P_{f}$ where is the volume and is the percent solution.

So the equation to solve becomes x(0) + 2(.80) = (x + 2)(.20) and x = 6 gallons of pure water needs to be added to get a 20% acid solution.

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SAT Math : Linear / Rational / Variable Equations

Study concepts, example questions & explanations for SAT Math

All SAT Math Resources

Example Questions

Example Question #31 : Linear / Rational / Variable Equations

Example Question #71 : How To Find The Solution To An Equation

Example Question #32 : Algebra

Example Question #33 : Algebra

Example Question #71 : How To Find The Solution To An Equation

Example Question #31 : Linear / Rational / Variable Equations

Example Question #43 : Linear / Rational / Variable Equations

Example Question #35 : Algebra

Example Question #1811 : Sat Mathematics

Example Question #37 : Algebra

All SAT Math Resources

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