**Lower Elementary**

*Question: *Brittany took 7 photos on Monday, 8 photos Tuesday as well as Wednesday, and 9 photos on Thursday. Brittany developed her pictures on Friday, but unfortunately dropped half of her photos in a puddle of water. If those pictures were ruined, how many pictures does she have left?

*Answer: *16 photos are left

*Solution: *Starting by adding all the photos Brittany took for the week.

7 + 8 + 8 + 9 = 32 photos

Since half of the photos were ruined we need to find a half of 32.

Half of 32 = Half of 30 + Half of 2 = 15 + 1 = 16 photos

**Upper Elementary**

*Question: *In 6 years David’s niece will be a quarter of David’s age. If his niece is 2 years old, how old is David now?

*Answer: *26 years old

*Solution: *In 6 years David’s niece will be 8 years old and David will be four times her age of 32 (4 × 8) Subtracting the 6 years we added initially, we find that David’s age now is 26.

**Middle School**

*Question: *Kendra bought a new purse that was marked down 25% from its original price. Kendra also used a coupon that takes 50% of the discounted price. If the purse originally costs $80, how much did she pay for it?

*Answer: *$30.00

*Solution: *First we find 25% of $80, then subtract it from $80. Because a quarter is a half of a half:

half of 80 = 40, half of 40 = 20, so a quarter of 80 is 20.

Subtracting 20 from 80 will give us the discounted price of 60.

Next we find the discount from the coupon. We need to find 50% or half of the discounted price. Half of 60 is 30, so we can conclude that the final price Kendra paid for her new purse is $30.00.

**Algebra and Up**

*Question: *The sides of the Great Pyramid in Giza have slopes that are approximately 1.28. The base of the square pyramid has a width of 230 meters. What is the width of the pyramid at the height of 68 meters? (Hint: Use a coordinate plane.)

*Answer: *123.75 meters

*Solution: *By drawing a pyramid with the centered at the origin, we can solve for the width at a height of 68 meters by using linear equations.

By the above diagram you can see that the base ends of the pyramid are at 115 and -115. Looking at the left half of the pyramid we can write a linear equation that solves for the total height of the pyramid.

y = 1.28x + b (1)

Plugging in the left point of the base the solving for b (the height of the pyramid):

0 = 1.28(-115) + b

b = 147.2 meters

Now that we know the height of the pyramid we can plug that into equation 1.

y = 1.28x + 147.2

Plugging the height into the y coordinate we can then solve for the x coordinate.

68 = 1.28x + 147.2

x = -61.875 meters

We get a negative value because the point on the pyramid is on the left side of the y-axis.

Finding the distance between the two points give us our answer of 123.75 meters.