**Lower Elementary:**

*Question: *Emma has a stamp collection. The first page has 3 stamps, second page 5 stamps, third page 4 stamps, fourth page 6 stamps, fifth page 5 stamps, sixth page 7 stamps, and so on. If this pattern continues, how many stamps will there be on the tenth page?

*Answer: *9 stamps

*Solution: *The pattern on the pages goes 3, 5, 4, 6, 5, 7… The pattern is adding 2, and then subtracting 1. If we continue the pattern, the seventh page would have 6 stamps. The eighth page would have 8 stamps. The ninth page would have 7 stamps, and the tenth page would have 9 stamps. So the tenth page would have 9 stamps.

**Upper Elementary:**

*Question: *A charity is having a comedy show fundraiser that is taking place at a theater that seats 5,000 people. They sold 90% of the tickets. Each ticket costs $10. How much money did the charity make?

*Answer: *$45,000

*Solution: *First, find how many tickets the charity sold. 90% of 5,000 is 4,500 (percent is for each hundred and there are 50 hundreds in 5,000, so 90 × 50 = 4,500). They sold 4,500 tickets. Now multiply that by the cost of each ticket to get the total amount the charity made. 4,500 × 10 = $45,000.

**Middle School:**

*Question: *What is half of two-thirds of three-fourths of four-fifths of five-sixths of six-sevenths of seven-eighths of eight?

*Answer: *1

*Solution: *Written out, this expression becomes:

1/2 × 2/3 × 3/4 × 4/5 × 5/6 × 6/7 × 7/8 × 8

Notice that for each fraction, the denominator cancels with the numerator of the next fraction. So if we cancel each of the fractions, our problem becomes:

1/8 × 8

One-eighth of 8 is 1.

**Algebra and Up:**

*Question: *Robin buys 2 apples and 3 bananas for $7. Scott buys 4 apples and 2 bananas for $8. How much does one apple and one banana cost separately?

*Answer: *Apple: $1.25 Banana: $1.50

*Solution: *Let a = the cost of 1 apple and let b = the cost of 1 banana. Written as a system of equations, the problem becomes:

2a + 3b = 7

4a + 2b = 8

One way to solve this problem is to use elimination. If we divide the second equation by 2, we have:

2a + 3b = 7

2a + b = 4

Subtract the second equation from the first to cancel the a’s:

2b = 3

b = 1.5

So one banana costs $1.50. Plug it into either equation to solve for a. Let’s plug it into the second equation:

4a + 2(1.5) = 8

4a + 3 = 8

4a = 5

a = 1.25

So one apple costs $1.25.