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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?
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- If Trent used 3 times as much lemonade as grape juice then he used ____ cups of lemonade and ____ cups of grape juice.
- Yaara removed _____ of the punch. So the remaining punch has = _____ cups of lemonade
- She also removed ____ of the grape juice, so the remaining punch has _____ cups of grape juice.
- After she adds the cup of grape juice, the punch contains _____ cups of grape juice and _____cups of lemonade.
- The ratio of lemonade to grape juice is ______
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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?
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- Call the 3 dimensions of the box a, b and c
- The 3 sides are a x b, a x c, and b x c
- The factors of the 3 sides' areas are:
96 =
252 =
168 =
- Reduce these to only those factors shared by at least one other side:
96 =
252 =
168 =
- The dimensions must be combinations of these factors.
Here are the possible combinations:
96 sq. cm,:
252 sq. cm.:
168 sq. cm.:
- Resolve the 96 sq. cm. side because it is the easiest = (____ x ____)
- With the 96 sq. cm. side resolved, the only solution for the other sides are (____ x ____) and (____ x ____)
- The 3 dimensions are ____ ____ and ____
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