Hands-on math!

Washington State Math Olympiad
Hints and Solutions
2012 Grade 7 Measurement
Problem
1) Trent has made 10 cups of punch by using three times as much lemonade as grape juice. Yaara drinks 1 cup and then realizes that Trent needs a full 10 cups of the punch. She tried to help by adding 1 cup grape juice to the pitcher. What is the ratio of lemonade to grape juice in the punch, using whole numbers in both parts of the ratio?

2) Sally and Yvonne wanted to make a rectangular toy box out of plywood. At the lumber yard, they realized that they had forgotten the dimensions of the box. Sally remembered that one of the sides had an area of 96 square centimeters. Yvonne remembered that the other sides had areas of 252 and 168 square centimeters. What are the dimensions of the box?

3) A man walks for 15 minutes to catch a bus. He rides the bus for 5 miles. The bus is going 30 miles per hour. How long does his total journey take? Answer in minutes.

Problem
4) It takes Bobby 1 hour and 15 minutes to mow his grandma's lawn, see figure. If Bobby mows at the same rate, how long will it take him to mow his uncle's field which has an area of 5000 square feet? Express your answer in hours and minutes rounded to the nearest minute.

5) Toni needs 3 gallons of paint. Two brands, Color Fine and Purity, have the same price in the store, but she has a coupon for 15% off on the Purity brand. Sales tax is 10%. If the original price is $26 per 1 gallon can, how much will she save overall if she buys the Purity brand? (Note: the sales tax is added after the discount is taken.)