Difference between revisions of "1996 AJHSME Problems/Problem 7"
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<math>\text{5 / 4096 / 4096}</math> | <math>\text{5 / 4096 / 4096}</math> | ||
| − | You could create a similar table without doing all of the calculations by converting all the goldfish into powers of <math>2</math>. In this table, you could increase Brent's goldfish by two powers of <math>2</math>, while increasing | + | You could create a similar table without doing all of the calculations by converting all the goldfish into powers of <math>2</math>. In this table, you could increase Brent's goldfish by two powers of <math>2</math>, while increasing Gretel's fish by one power of <math>2</math>. |
Either way, in <math>5</math> months they will have the same number of fish, giving an answer of <math>\boxed{B}</math> | Either way, in <math>5</math> months they will have the same number of fish, giving an answer of <math>\boxed{B}</math> | ||
Revision as of 11:48, 24 October 2016
Problem
Brent has goldfish that quadruple (become four times as many) every month, and Gretel has goldfish that double every month. If Brent has 4 goldfish at the same time that Gretel has 128 goldfish, then in how many months from that time will they have the same number of goldfish?
Solution
Call this month "Month 0". Make a table of the fish that Brent and Gretel have each month.
You could create a similar table without doing all of the calculations by converting all the goldfish into powers of 
. In this table, you could increase Brent's goldfish by two powers of , while increasing Gretel's fish by one power of .
Either way, in 
months they will have the same number of fish, giving an answer of 
See also
| 1996 AJHSME (Problems • Answer Key • Resources) | ||
| Preceded by Problem 6 |
Followed by Problem 8 | |
| 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. 
