High School Math : Equations

Example Questions

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Example Question #31 : Equations

is what percent of ?

Explanation:

Verbal cues include "IS" means equals and "OF" means multiplication.

So the equation to solve becomes

and dividing both sides by gives

Example Question #6 : Solving Equations

Solve the system of equations.

None of the other answers are correct.

Explanation:

Isolate  in the first equation.

Plug into the second equation to solve for .

Plug into the first equation to solve for .

Now we have both the and values and can express them as a point: .

Example Question #7 : Solving Equations

Solve for  and .

Cannot be determined.

Explanation:

1st equation:

2nd equation:

Subtract the 2nd equation from the 1st equation to eliminate the "2y" from both equations and get an answer for x:

Plug the value of  into either equation and solve for :

Example Question #32 : Equations

Solve for :

Explanation:

Rewrite  as a compound statement and solve each part separately:

Therefore the solution set is .

Example Question #33 : Equations

Solve the following equation for :

Explanation:

The first step in solving this equation is to distribute the 3 and the 4 through the parentheses:

Simplify:

Now, we want to get like terms on the same sides of the equation. That is, all of the terms with an  should be on one side, and those without an  should be on the other. To do this, we first subtract  from both sides:

Simplify:

Now, we subtract 6 from both sides:

Example Question #34 : Equations

Goldenrod paint is made by mixing one part red with three parts yellow.  How many gallons of yellow paint should be mixed with two quarts of red paint?

Explanation:

This problem is solved using proportions and the following conversion factor:

Let yellow quarts of paint.

Then cross multiply to get .

Example Question #35 : Equations

Solve for :

Explanation:

Multiply both sides by to eliminate the fractions to get .

Then use the distributive property to get .

Now subtract from both sides to get .

Now subtract from both sides to get .

Example Question #36 : Equations

To mail a package, there is an initial charge of  to cover the first ounce, with another for each additional ounce.  How much does it cost to mail a half pound package?