Difference between revisions of "2020 AMC 8 Problems/Problem 1"
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==Solution== | ==Solution== | ||
Luka will need <math>3\cdot 2=6</math> cups of sugar and <math>6\cdot 4=24</math> cups of water. The answer is <math>\boxed{\textbf{(E) } 24}</math>. | Luka will need <math>3\cdot 2=6</math> cups of sugar and <math>6\cdot 4=24</math> cups of water. The answer is <math>\boxed{\textbf{(E) } 24}</math>. | ||
| + | |||
| + | ==Solution 2== | ||
| + | LEt <math>W, S,</math> and <math>L</math> represent the cups of water, sugar, and lemon juice Luka needs for his recipe. We are given that <math>W=4S</math> and <math>S=2L</math>. Since <math>L=3</math>, it follows that <math>S=6</math>, which in turn implies that <math>W=24 </math>\implies\boxed{\textbf{(E) }24}$.<br> | ||
| + | ~jmansuri | ||
==See also== | ==See also== | ||
{{AMC8 box|year=2020|before=First problem|num-a=2}} | {{AMC8 box|year=2020|before=First problem|num-a=2}} | ||
{{MAA Notice}} | {{MAA Notice}} | ||
Revision as of 03:37, 18 November 2020
Luka is making lemonade to sell at a school fundraiser. His recipe requires 
times as much water as sugar and twice as much sugar as lemon juice. He uses 
cups of lemon juice. How many cups of water does he need?
Solution
Luka will need 
cups of sugar and 
cups of water. The answer is 
.
Solution 2
LEt 
and 
represent the cups of water, sugar, and lemon juice Luka needs for his recipe. We are given that 
and 
. Since 
, it follows that 
, which in turn implies that 
\implies\boxed{\textbf{(E) }24}$.
~jmansuri
See also
| 2020 AMC 8 (Problems • Answer Key • Resources) | ||
| Preceded by First problem |
Followed by Problem 2 | |
| 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 | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
