2014 AMC 10A Problems/Problem 6
- The following problem is from both the 2014 AMC 12A #4 and 2014 AMC 10A #6, so both problems redirect to this page.
Problem
Suppose that 
cows give 
gallons of milk in 
days. At this rate, how many gallons of milk will 
cows give in 
days?
Solution 1
We need to multiply by 
for the new cows and 
for the new time, so the answer is 
, or 
.
Solution 2
We plug in 
, 
, 
, 
, and 
. Hence the question becomes "2 cows give 3 gallons of milk in 4 days. How many gallons of milk do 5 cows give in 6 days?"
If 2 cows give 3 gallons of milk in 4 days, then 2 cows give 
gallons of milk in 1 day, so 1 cow gives 
gallons in 1 day. This means that 5 cows give 
gallons of milk in 1 day. Finally, we see that 5 cows give 
gallons of milk in 6 days. Substituting our values for the variables, this becomes 
, which is 
.
Solution 3
We see that the the amount of cows is inversely proportional to the amount of days and directly proportional to the gallons of milk. So our constant is 
.
Let 
be the answer to the question. We have 
See Also
| 2014 AMC 10A (Problems • Answer Key • Resources) | ||
| Preceded by Problem 5 |
Followed by Problem 7 | |
| 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 AMC 10 Problems and Solutions | ||
| 2014 AMC 12A (Problems • Answer Key • Resources) | |
| Preceded by Problem 3 |
Followed by Problem 5 |
| 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 AMC 12 Problems and Solutions | |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
