**Lower Elementary**

*Question: *Jeffery had 10 action figures and then he lost 4 of them. If Alex had 8 action figures then bought 6 more, how many more action figures does Alex have than Jeffery?

*Answer: *8 action figures

*Solution: *Jeffery lost 4 of his 10 action figures. 4 less than 10 is 6 (10 – 4 = 6) so we know that Alex now has 6 action figures. Alex had 8 action figures then bought 6 more. To go from 8 up to 10 we add 2 from the 6 and then we add the 4 remaining to the 10 to get 14. Alex now has a total of 14 action figures. Finally, to find how many more action figures Alex has than Jeffery, we need to find the difference between 6 and 14. Subtracting gives, 14 – 6 = 8. Alex has 8 more action figures than Jeffery.

**Upper Elementary**

*Question: *This Friday is April 13th. What day of the week and what day of the month will it be in 25 days?

*Answer: *Tuesday, May 8th

*Solution: *7 days from Friday will be Friday, so 21 days from Friday will also be Friday. 4 days after Friday will be Tuesday.

Starting from Friday: Saturday → Sunday → Monday → Tuesday

There are 30 days in April. On Friday, April 13th, there are 17 days left in April (30 – 13 = 17). Because a part is equal to the whole minus the other part, we subtract the other part (17) from the whole (25) to find the part, or how many days are left.

25 – 17 = 8

This means 25 days from April 13th leaves us with 8 days in May, which is May 8th.

**Middle School**

*Question: *Train A leaves a leaves the station the same time as Train B traveling in the same direction. Train B, travels 75 mph and Train A travels at 51 mph. How many hours would it take for Train A and Train B to be 126 miles apart?

*Answer: *5.25 hours

*Solution: *Every hour Train B is 24 miles farther ahead of Train A (75 – 51 = 24). To find how many hours it takes for the distance between the two trains to 126 miles, we need to find how many 24s fit into 126. This is done by dividing 24 into 126.

126 ÷ 24 = 5.25 hours

Another way to solve this problem is using the distance formula (*d* = *rt*).

Train A:

*d*_{A} = *r*_{A}*t*_{A} = 51*t*_{A}

Train B:

*d*_{B} = 75*t*_{B}

Subtracting *d*_{A} from *d*_{B} will leave us with the distance between the two trains. In this problem we are trying to find how many hours it takes for the trains to be 126 miles apart. It is also important to note that when the trains are 126 miles apart, *t*_{A} = *t*_{B} = *t*.

75*t* – 51*t* = 126

24*t* = 126

*t* = 5.25 hours

**Algebra and Up**

*Question: *On average, David drives 1540 miles a month. Currently David’s car gets, on average, 21 miles per gallon. He is thinking about buying a hybrid car capable of 55 miles per gallon. If gas costs $3.95 per gallon, how much money would David save in gas each month if he were to switch to a hybrid car?

*Answer: *$179.07

*Solution: *In one month, David’s current car uses 73â…“ gallons of gas (1540 / 21 = 73â…“). Gas at $3.95 a gallon, currently David spends $289.67 a month on gas (73â…“ â— $3.95 = $289.67).

If David were driving the hybrid car he would use 28 gallons of gas a month (1540 / 55 = 28) and would spend $110.06 a month on gas (28 â— $3.95 = $110.06).

We can conclude that if David switched to driving a hybrid car he would save $179.07 a month in gas ($289.67 – $3.95 = $179.07).