**Lower Elementary**

*Question: *Sammy has twice as many marbles as Jimmy. Jimmy has 3 marbles more than Molly. If Molly has 6 marbles, how many marbles does Sammy have?

*Answer: *18 marbles

*Solution: *Starting with Molly and working back toward Sammy. Jimmy has 3 more marbles than Molly, so Jimmy has 9 marbles (6 + 3). Because Sammy has twice the amount of marbles as Jimmy, Sammy has 18 marbles (9 + 9).

**Upper Elementary**

*Question: *Jim is 6 inches taller than Bill. If Bill is 4 feet 7 inches tall, how tall is Jim?

*Answer: *5 feet and 1 inch

*Solution: *Because Jim is 6 inches taller than Bill, we add 6 inches to Bill height. We can only add things of the same name so adding 7 inches and 6 inches give us 13 inches. Because there are 12 inches in a foot, 13 inches is equal to 1 foot 1 inch. Adding this to 4 feet gives us 5 feet 1 inch.

4 feet 7 inches

__+ 6 inches__

5 feet 1 inches

**Middle School**

*Question: *Two identical triangles, each with a base of 7 inches and a height of 15 inches are cut from a single piece of cardboard with an area of 215 square inches. What is the remaining area of the cardboard after the triangles are cut out?

*Answer: *110 in^{2}

*Solution: *Because a part is the whole minus the other parts, we can subtract the triangles (the other parts) from the cardboard (the whole), to find the remaining cardboard (the part).

We start by finding the area of the triangles.

A = ½bh = ½(7)(15) = ½(105) = 52.5 square inches

Because we have 2 identical triangles, we double the area to count for both triangles.

52.5 square inches doubled = 105 square inches

Another approach would be to understand that two identical triangles put together form a parallelogram. The area of a parallelogram is base x height.

A = 15 × 7 = 105 square inches

Lastly we subtract the area of the both triangles (the other parts) from the cardboard (the whole) to find the remaining cardboard (the part).

215 in^{2} – 105 in^{2} = 110 in^{2}

**Algebra and Up**

*Question: *The SR-71 Blackbird was used during the cold war as a spy plane. With a max speed of Mach 3.5, it is the fastest manned aircraft in the world (other than the space shuttle). A Mach number is defined as the ratio of the speed of an aircraft to the speed of sound (about 761 mph). At its max speed, how long would it take the SR-71 to travel the 2443.79 miles from Los Angeles to New York City? Round answer to the nearest hundredth of an hour.

*Answer: *0.92 hours

*Solution: *In order to solve this problem we need to first find how fast Mach 3.5 is in miles per hour. We do this by multiplying 3.5 by the speed of sound, 761 mph.

3.5 â— 761 mph = 2663.5 mph

Now we find, at that speed, how long it would take the SR-71 to travel 2443.79 miles.

2443.79 miles / 2663.5 mph = 0.92 hours