1996 AJHSME Problems/Problem 7
Contents
[hide]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 1
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
Solution 2
Create two equations.
Brent starts with goldfish and they quadruple each month, giving us or .
Gretel starts with goldfish and they double each month, giving us or .
Using substitution, . Thus giving us , which is .
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 |
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