**Lower Elementary:**

*Question: *It took Bobby 7 tries on the crane machine to get a stuffed animal. Each try took 50¢. If Bobby started with $5, how much money does he have left?

*Answer: *$1.50

*Solution: *First we need to find out how much Bobby spent getting the stuffed animal. Each try is 50¢ and it took Bobby 7 tries. So, we count by 50, 7 times. 50, 100, 150, 200, 250, 300, 350. Bobby spent $3.50 on the crane machine. Since he started with $5, to find out how much he has left, subtract 3.50 from 5. 5 – 3.50 = 1.50. Bobby has $1.50 left.

**Upper Elementary:**

*Question: *Kelly has 20 DVDs. 1/5 of the DVDs are comedy movies, 1/2 of the DVDs are action movies, and the rest are horror movies. How many horror movies does Kelly have?

*Answer: *6 horror movies

*Solution: *One way to solve this problem is to see how many DVDs Kelly has of each movie genre. 1/5 of 20 is 4, so Kelly has 4 comedy movies. 1/2 of 20 is 10, so Kelly has 10 action movies. That means that Kelly has 14 movies that are action and comedy. Since she has a total of 20 movies, the remaining 6 movies must be horror movies (20 – 14 = 6).

**Middle School:**

*Question: *One hundred twenty times a number x raised to the fifth power times another number y raised to the sixth power is divided by the quantity of eighty times the number y to the fourth power times another number z raised to the third power. What is this expression in simplest form?

*Answer: *3x^{5} y^{2}/(2z^{3})

*Solution: *First, we have to translate the word expression into the number expression. Doing this we have:

120x^{5}y^{6}/(80y^{4}z^{3})

First we can simplify the numbers 120/80, which we can divide them both by 40 to get 3/2.

3x^{5}y^{6}/(2y^{4}z^{3})

There is a y on the top and the bottom, so we can simplify by cancelling the y. Recall that when dividing numbers raised to exponents we subtract the exponents.

3x^{5}y^{2}/(2z^{3})

There is nothing else we can simplify, so that is the simplest form of the expression.

**Algebra and Up:**

*Question: *Where do the lines y = 3x + 2 and 4x + 3y = 32 intersect?

*Answer: *(2, 8)

*Solution: *To find where the lines intersect, we have to find the same coordinate that satisfies both equations. One way to do this is to substitute y = 3x + 2 into the other equation.

4x + 3(3x + 2) = 32

Distribute the 3.

4x + 9x + 6 = 32

Combine the like terms.

13x + 6 = 32

Subtract 6 from both sides.

13x = 26

Divide both sides by 13.

x = 2

We know what x is, so now we substitute that value into either equation to solve for y. Let’s substitute it into the equation y = 3x + 2.

y = 3(2) + 2

Multiply.

y = 6 + 2

Add.

y = 8

The point at which both likes intersect is (2, 8).