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 coi
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Question 149607: 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. Answer by Fombitz(32388) (Show Source):
You can put this solution on YOUR website! D-dimes
Q-quarters
H-half dollars
1. Total count of coins.
2. Total value of coins.
3. Three times dimes equals quarters.
Use eq. 3 to substitute for Q in eq. 1 and 2.
1.
We'll call that equation 1a.
1a.
.
.
.
.
2.
First multiply by 100 to get rid of decimals.
We'll call that equation 2a.
2a.
Use eq. 1a to come up with an expression for H as a function of D.
1a.
Now substitute into eq. 2a,
2a.
From eq. 3,
From 1a,
There are 15 dimes, 45 quarters, and 10 half dollars.
