# PSAT Math : How to find the solution to an equation

## Example Questions

### Example Question #1 : How To Find Out When An Equation Has No Solution

Solve for .

No solutions.

No solutions.

Explanation:

Cross multiplying leaves , which is not possible.

### Example Question #131 : Gre Quantitative Reasoning

If is defined for all numbers  and  to be  , then what is ?

Explanation:

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

### Example Question #131 : Algebra

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?

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 #42 : Linear / Rational / Variable Equations

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

Explanation:

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

### Example Question #131 : Gre Quantitative Reasoning

With a  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?

Explanation:

In general,

The distance is the same going and coming; however, the head wind affects the rate.  The equation thus becomes .

Solving for  gives .

### Example Question #31 : How To Find The Solution To An Equation

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

Explanation:

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

in general where  is the volume and  is the percent.

So the equation to solve becomes

and

### Example Question #211 : Algebra

Solve  and

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  to get  and then substutite the  into the second equation to get

Solving this equation gives  and substituting this value into one of the original equations gives , thus the correct answer is .