Difference between revisions of "2009 AMC 8 Problems/Problem 15"
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==Problem== | ==Problem== | ||
− | A recipe that makes <math> 5</math> servings of hot chocolate requires <math> 2</math> squares of chocolate, <math> \frac{1}{4}</math> cup sugar, <math> 1</math> cup water and <math> 4</math> cups milk. Jordan has <math> 5</math> squares of chocolate, <math> 2</math> cups of sugar, lots of water and <math> 7</math> cups of milk. If | + | A recipe that makes <math> 5</math> servings of hot chocolate requires <math> 2</math> squares of chocolate, <math> \frac{1}{4}</math> cup sugar, <math> 1</math> cup water and <math> 4</math> cups milk. Jordan has <math> 5</math> squares of chocolate, <math> 2</math> cups of sugar, lots of water, and <math> 7</math> cups of milk. If he maintains the same ratio of ingredients, what is the greatest number of servings of hot chocolate he can make? |
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==Solution== | ==Solution== | ||
− | + | Assuming excesses of the other ingredients, the chocolate can make <math>\frac52 \cdot 5=12.5</math> servings, the sugar can make <math>\frac{2}{1/4} \cdot 5 = 40</math> servings, the water can make unlimited servings, and the milk can make <math>\frac74 \cdot 5 = 8.75</math> servings. Limited by the amount of milk, Jordan can make at most <math>\boxed{\textbf{(D)}\ 8 \frac34}</math> servings. | |
==See Also== | ==See Also== | ||
{{AMC8 box|year=2009|num-b=14|num-a=16}} | {{AMC8 box|year=2009|num-b=14|num-a=16}} | ||
+ | {{MAA Notice}} |
Latest revision as of 19:53, 20 August 2020
Problem
A recipe that makes servings of hot chocolate requires
squares of chocolate,
cup sugar,
cup water and
cups milk. Jordan has
squares of chocolate,
cups of sugar, lots of water, and
cups of milk. If he maintains the same ratio of ingredients, what is the greatest number of servings of hot chocolate he can make?
Solution
Assuming excesses of the other ingredients, the chocolate can make servings, the sugar can make
servings, the water can make unlimited servings, and the milk can make
servings. Limited by the amount of milk, Jordan can make at most
servings.
See Also
2009 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by Problem 14 |
Followed by Problem 16 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
All AJHSME/AMC 8 Problems and Solutions |
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