SOLUTION: 12. 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
(
Algebra ->
Equations
-> SOLUTION: 12. 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
(
Log On
Question 339469: 12. 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
Please explain the above problem. Would really appreciate.
Thanks Found 2 solutions by jrfrunner, josmiceli:Answer by jrfrunner(365) (Show Source):
You can put this solution on YOUR website! let F=Number of $5 bills
let T=Number of $10 bills
--
Given
expression 1: T < F
expression 2: 5*F+10*T=460
---
Solve for F in the second expression
F=(460-10*T)/5=92-2*T
--
since we know that T is less than F then
3*T<92
T<92/3=30.667 but since we are dealing with whole numbers
T=30
substituting T=30 in F=92-2*T=92-60=32
--
lets check
Choose values of T around T=30
if T=29 then F=92-2*29=34 So
if T=31 then F=92-2*31=30 but no longer holds true
--
so the pivot point for is T=30 which means F=32
You can put this solution on YOUR website! Let = the number of $5 bills she had
Let = the number of $10 bills she had
given:
--------------
Note that there has to be an even number of $5 bills
to get $460
What would and be if
This doesn't work, since needs to be an integer
I'll try
Substituting: doesn't work
I'll try
substituting:
This looks like isthe smallest number of $5's that
will give me $460 and still have more $5's than
$10's
check:
The answer is (A)
