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

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.

RELATED QUESTIONS
A collection of 70 coins consisting of dimes, quarters, and half-dollars has a value of... (answered by MathTherapy)

A collection of 70 coins consisting of dimes, quarters, and half-dollars has a value of... (answered by jorel1380)

A collection of 65 coins consisting of dimes, quarters, and half-dollars has a value of... (answered by CharlesG2)

A collection of 42 coins consisting of dimes, quarters, and half-dollars has a value of... (answered by josmiceli)

A coin collection has 22 coins consisting of quarters and dimes. There are two more dimes (answered by lynnlo)

G'day, Thanks in advance for taking the time to answer my question. Here it is:... (answered by TimothyLamb,josgarithmetic,MathTherapy)

A collection of 33 coins, consisting of nickels, dimes, and quarters, has a value of... (answered by mananth)

A collection of 70 coins consisting of dimes, quarters, and half dollars has a value of... (answered by stanbon)