SOLUTION: Frank has 24 dimes and nickels. Rick has 2/3 as many nickels and 1 1/2 times as many dimes as Frank has. If Rick and Frank have the same amount of money, how much does each of th

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Question 119080: Frank has 24 dimes and nickels. Rick has 2/3 as many nickels and 1 1/2 times as many dimes as Frank has. If Rick and Frank have the same amount of money, how much does each of them have?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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Frank has 24 dimes and nickels. Rick has 2/3 as many nickels and 1 1/2 times as many dimes as Frank has. If Rick and Frank have the same amount of money, how much does each of them have?
:
Let x = no. of Franks dimes
Then
(24-x) = no of Franks nickels
:
3%2F2x = no. of Ricks dimes
and
2%2F3(24-x) = no. of Ricks nickels
:
It says they have the same amt of money, write an equation from this fact:
:
.10x + .05(24-x) = .10*3%2F2x + .05*2%2F3(24-x)
:
.1x + 1.2 - .05x = .3%2F2x + .1%2F3(24-x)
:
+.05x + 1.2 = .3%2F2x + .1%2F3(24-x)
:
Multiply equation by 6 to get rid of the denominators
6(.05)x + 6(1.2) = 6*.3%2F2x + 6*.1%2F3(24-x)
:
.3x + 7.2 = .9x + .2(24-x)
:
.3x + 7.2 = .9x + 4.8 - .2x
:
.3x + 7.2 = .7x + 4.8
:
7.2 - 4.8 = .7x - .3x
:
2.4 = .4x
:
x = 2.4/.4
:
x = 6 dimes (Frank)
Then
(24-6) = 18 nickels (Frank)
:
Franks total:
.10(6) + .05(18) =
.60 + .90 = $1.50
:
Rick:
3%2F2*6 = 9 dimes (Rick)
2%2F3*18 = 12 nickels (Rick)
:
Ricks total:
.10(9) + .05(12) =
.90 + .60 = $1.50
:
Equal so:
Frank had 6 dimes 18 nickels
Rick had 9 dimes and 12 nickels