SAT Math : How to find the solution to an equation

Study concepts, example questions & explanations for SAT Math

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Example Questions

Example Question #61 : How To Find The Solution To An Equation

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

Possible Answers:

Correct answer:

Explanation:

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

Example Question #121 : Equations / Inequalities

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:

Correct answer:

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

.

Example Question #134 : Algebra

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

Possible Answers:

Correct answer:

Explanation:

If we take the units and look at division,  will yield hours as a unit. Therefore the answer is .

Example Question #135 : 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:

125\ mph

300\ mph

175\ mph

275\ mph

225\ 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.

Example Question #122 : Equations / Inequalities

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

Possible Answers:

2.4\ L

1.2\ L

1.5\ L

1.6\ L

0.8\ 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

Example Question #91 : Linear / Rational / Variable Equations

Solve x+2y=14 and 2x+y=13

Possible Answers:

(4,5)

(3,2)

(-4,-5)

(1,3)

(5,4)

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).

Example Question #31 : Algebra

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:

1

2

5

4

3

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.

Example Question #131 : Algebra

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

Possible Answers:

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

x=-8

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

x=8

x=-\frac{2}{3}

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 )

Example Question #141 : Algebra

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

 and solving shows that he needs to sell 13 cars to make $7,500.

Example Question #123 : Equations / Inequalities

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:

Correct answer:

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  and  gallons of pure water needs to be added to get a 20% acid solution.

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