Let  = number of dimes,  = number of nickels, and 

= number of quarters.

The general equation to use is:

where  is the money value and  is the number of coins

So the equation to solve becomes

Thus, solving the equation shows that she had five nickels, four dimes, and three quarters giving a total of 12 coins.

Pure water is 0% and pure solution is 100%

where  is the volume and  is the percent.

So the equation to solve becomes

So we need to add  pure water to of 80% cleaning solution to yield 25% cleaning solution.

We are looking for the value of t  that gives $675 as the result when plugged in V (t ). While there are many ways to do this, one of the fastest is to plug in the answer choices as values of t .

When we plug t  = 1 into V (t ), we get V (1) = 1200(0.75)¹ = 1000(0.75) = $900, which is incorrect.

When we plug t  = 2 into V (t ), we get V (2) = 1200(0.75)² = $675, so this is our solution.

The value of the tractor will be $675 after 2 years.

Finally, we can see that if t  = 3, 4, or 5, the resulting values of the V (t ) are all incorrect.

First combine like terms. In this case, 4x and 9x can be added together:

13x + 13 = 0

Subtract 13 from both sides:

13x = -13

Divide both sides by 13 to isolate x:

x = -13/13

x = -1

The total weight of the first three dogs is 225 pounds. This amount, plus the weight of the fourth dog, divided by total number of dogs, is the new average weight:

Let  the number of bird houses sold each month.

The break-even point is where the revenue is the same as the costs:

Solve for :

Therefore, Pets Plus must sell 30 bird houses to break-even.

Let  = the number of birdhouses sold each month.

Substituting in 50 for  gives an answer of 500, so the profit on 50 birdhouses is $500.

Let  = Joey's age and  = George's age.

Then the equation to solve becomes .

Therefore, Joey is 4 years old and George is 12 years old, so the product of their ages is 48.

Let  = 1st even number, = 2nd even number, and  = 3rd even number.

Then the equation to solve becomes .

Thus , so the middle number is 14.

The quantity inside the absolute value brackets must equal either  or , depending on whether the quantity inside the brackets is positive or negative. We therefore have two seperate equations:

To solve the first equation, add 9 to both sides:

Subtract  from both sides:

This is the first solution. Now let's look at the second equation. The distributive law gives us:

Add 9 to both sides:

Add  to both sides:

Divide both sides by 3:

Therefore, is either 4 or 6. 

Statement  does NOT have to be true because  can also equal 4.

Statement  must be true because both 4 and 6 are positive .

Finally, statement  always holds because 4 and 6 are both even.