SOLUTION: A collection of 70 coins consisting of dimes, quarters, and half-dollars has a value of $17.75. There are three times as many quarters as dimes. Find the number of each kind of c
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Question 177878This question is from textbook
: A collection of 70 coins consisting of dimes, quarters, and half-dollars has a value of $17.75. There are three times as many quarters as dimes. Find the number of each kind of coin. This question is from textbook
You can put this solution on YOUR website! Let the amount of dimes be d, then the amount of quarters are 3d
Let the amount of half-dollars be h
Then d + 3d + h = 70, or 4d + h = 70
Then d(.10) + 3d(.25) + h(.5) = 17.75, or .1d + .75d + .5h = 17.75, or .85d + .5h = 17.75
4d + h = 70 -----------(i)
.85d + .5h = 17.75 -------(ii)
Multiply eq. (i) by - .5 -2.00d - .5h = - 35 -------(iii)
Add eq (ii) & (iii) -1.15d = - 17.25
d = 15
4(15) + h = 70
60 + h = 70
h = 10
Therefore, there are 15 dimes - $1.50
there are 45 quarters - $11.25
there are 10 half-dollars - $5.00
