Lower Elementary
Question: Fred decided to ride the bus to the mall to meet his friends. Fred is the only one who gets on the bus at his stop. Before he got on the bus there were 10 men, 15 women, and 8 children. At the next stop, 2 women and 3 men get off and 4 women and 2 children get on. At the next stop, 3 men, 1 woman and 1 child get off and 4 men and 1 woman get on. At the next stop, Fred gets off with 2 other men, 3 women and 4 children. How many people are still on the bus after Fred got off the bus?
Answer: 25 people
Note: The bus driver was accounted for in the original number of people who were on the bus.
Upper Elementary
Question: Amanda paid $13.50 dollars for a sweater that was on sale for 50% off the original price, and she used a coupon that gave her an extra $10.00 off the sale price. What was the original price of the sweater?
Answer: $47.00
Note: Ignore tax.
Middle School
Question: Marianne is working on the set for a school play. She has to paint 250 identical rectangular boxes with red paint so they will look like bricks. She has two pints of red paint, that each cover 75 square feet. If each box is 6 inches long, 6 inches wide, and 3 inches tall, how many boxes can she paint?
Answer: 150 boxes
Note: That the surface area of each block is the sum of the area of its faces. The top and bottom of each box is 6 inches by 6 inches. 6 in. = 1/2 foot. So the area of the top/bottom is 1/4 sq. ft. Together that is 1/2 sq. ft. Each side of the four sides of the box is 3 inches by 6 inches. 3 in. = 1/4 foot. So the each side is 1/2 x 1/4 = 1/8 sq. ft. Together that is 1/2 sq. ft. The area of the entire box is 1 sq. ft. If each can covers 75 sq. ft. Then each will cover 75 boxes. Both cans will cover 150 boxes.
Algebra and Up
Question: If a is 30% smaller than b, b is 25% larger than c, and c is 20% larger than d, then what percentage larger than d is a?
Answer: 5%
Note: If a is 30% smaller than b, then a is 70% of b so a = .7b. b is 25% larger than c so b = 1.25c, and finally c is 20% larger than d so c = 1.2d. Using substitution we find that a = 1.05d. So a is 5% larger than d.
Solution: a = .7b, b = 1.25c, c = 1.2d
We solve the second equation for c and substitute into the 3rd equation. c = b/1.25
b/1.25 = 1.2 d => b = 1.5d
We solve the first equation for b and substitute it into this equation.
b = a/.7 => a/.7 = 1.5d
a = 1.05d
1.05d – d = 0.05 = 5%
