111 = n. 148 n = 3. 25

Transcription

1 Green Proportions n n 111 n 148 n n 6 90 n 4. A 10-foot stick casts a shadow of 8 feet and a nearby tree casts a shadow of 82 feet. How tall is the tree? 5. A family pays their 9 year old son an allowance of $5. If they want to keep the same age to allowance ratio, what allowance should they give their 8 year old son? 6. A model of an Egyptian pyramid has a scale of 1.2 inches:38 feet. If the height of the model is 3 inches, what is the height of the real pyramid? 7. Kristen is trying to guess Dan's height. He gave Kristen one clue: The ratio of my height to my father s height is 5:6 and my father is 68 inches tall. How tall is Dan? 8. Jody has a favorite drink she makes that is 3 parts lemonade and 5 parts cranberry juice. If she is making the drink for a party and wants to fill a 60-cup bowl, how much lemonade would she put in the bowl? 9. A trophy is made up of copper and nickel. The ratio of their weights is 6:11 respectively. If the amount of copper in the trophy is 48 pounds, how much does the trophy weigh? 1

2 10. Diane is making a large batch of soap. The recipe is as follows: 200 pounds of lye 25 pounds of fragrance 125 pounds of olive oil pounds of coconut oil Diane should reduce the recipe because she only has 138 pounds of lye. What should she reduce the coconut oil to? 11. Mark, who is 5 feet tall, told his dad that he could tell his dad's height just by measuring his dad's shadow. Mark knew that his own shadow was 8 feet and his dad's shadow measured 10 feet. How tall is his dad? 12. If a person walks 32 feet in 10 seconds, how far will he go in 72 seconds? 13. If there are 65 boys in a classroom and the ratio of boys to girls is 13:15, how many students are in the class? 14. The population of the United States is 280 million. If 2 out of 3 Americans know who the vice-president is, how many Americans know who the vice-president is? 15. The perimeter of the triangle is 40 inches. If you wanted to construct a similar triangle with a perimeter of 50 inches, what would be the length of the shortest side of the triangle? A star football player has written into his contract that the ratio of his salary to the next highest paid player in the league will be 4:3. If the next highest player makes $3,900,000, how much is the star player's salary? 17. A statue is made of a mixture of copper and zinc in a ratio of 11:4 (copper to zinc). If the weight of the statue is 3165 pounds, what is the weight of the copper? 18. A famous baseball player has a home run/strike out ratio of 2:13. This means that for every two home runs he hits, he strikes out 13 times. How many home runs would he hit in a season in which he strikes out 234 times? 19. Lindsey wanted to find out how tall a tree was at her school. Lindsey knew that she is 5 feet tall and at 3:00 her shadow is 6 feet. The tree's shadow at 3:00 is 38 feet. How tall is the tree? 2

3 Solutions feet 5. $ feet inches cups pounds pounds 200 pounds ( recipe lye ) ( ) pounds recipe coconut oil 138 pounds ( Diane' s lye) n ( reduced coconut oil ) Cross-multiply: 200n 39,675 n pounds feet 3 inches 5 feet ( Mark ' s height ) ( ' ) n Dad s height 8 feet ( Shadow ) 10 ( Dad ' s shadow ) Cross-multiply: 8n 50 n 6.24 feet feet 32 feet n feet 10 seconds 72 seconds Cross-multiply: 10n 2304 n feet students 13 boys 65 boys 15 girls n girls Cross-multiply: 13n 975 n 75 girls 75 girls + 65 boys 140 students /3 million 2 know n 3 people 280 million Cross-multiply: 3n 560 million n 186 2/3 million 3

4 inches 7( shortest ) n 40 ( perimeter ) 3,900, 000 Cross-multiply: 40n 350 n 8.75 inches 16. $5,200,000 4( star ' s salary ) n 3( next highest ) 3,900,000 Cross-multiply: 3n 15,600,000 n $5,200, pounds 11 parts cooper n 15total parts 3165 weight of statue Cross-multiply: 15n 34,815 n 2321 pounds home runs 2(hom e runs ) n 13 ( strikeouts ) 234 ( strikeouts ) Cross-multiply: 13n 468 n 36 home runs feet 8 inches 5 feet ( Lindsey ' s height ) ( ' ) n tree s height 6 feet ( Lindsey ' s shadow ) 38 feet ( tree ' s shadow ) Cross-multiply: 6n 190 n 31 2/3 4

5 Bibliography Information Unit 5 Rates, Ratios, and Proportions Teachers attempted to cite the sources for the problems included in this problem set. In some cases, sources may not have been known. Problems Bibliography Information 4-19 Zaccaro, Edward. Challenge Math (Second Edition): Hickory Grove Press,