bmwhype2 wrote:
Erica has $460 in 5-and 10-dollar bills only. If she has fewer 10-than 5-dollar bills, what is the least possible number of 5-dollar bills she could have?
(A) 32
(B) 30
(C) 29
(D) 28
(E) 27
We can create the following equation in which f = the number of 5-dollar bills and t = the number of 10-dollar bills.
5f + 10t = 460
f + 2t = 92
If the number of 5-dollar bills and the number of 10-dollar bills are equal, i.e., f = t, then we have:
f + 2f = 92
3f = 92
f = 30⅔
Since f, the number of 5-dollar bills, must be a whole number, and f > t, f should be at least 31. Let’s check whether f can be 31t:
If f = 31, then 31 + 2t = 92 → 2t = 61 → t = 30.5. However, t must be whole number also, so f can’t be 31.
Now let’s check if f can be 32:
If f = 32, then 32 + 2t = 92 → 2t = 60 → t = 30. We see that t is a whole number and f > t. So, the least possible value of f is 32.
Answer: A
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