SOLUTION: A coin collection made up of quarters, nickels, and pennies contains a total of 275 coins. The number of quarters is 46 less than twice the number of nickels. The total face value

Question 244705: A coin collection made up of quarters, nickels, and pennies contains a total of 275 coins. The number of quarters is 46 less than twice the number of nickels. The total face value of the coins is $37.47. How many of each denomination are there?
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

Let

represent the number of quarters.

Let

represent the number of nickels.

Let

represent the number of pennies.

Then

is the value of the quarters in cents.

And

is the value of the nickels in cents.

And

is the value of the pennies in cents.

The total value of the coins, in dollars, is $37.47. Therefore the total value of the coins in cents is 3747.

There are 275 coins, so:

The number of quarters is 46 less than twice the number of nickels, so:

The face value of the coins, in cents, is 3747, so:

Now you have three equations in three variables. Solve the system. The coordinates of the ordered triple solution set,

are the answer to the question.

Hint: I would proceed by eliminating the

variable in the first and third equations by substitution of the expression equal to

in the second equation. After simplifying both the new equations for the first and third and putting them into standard form, I would multiply either one of them by -1 and then solve for

by elimination of

.

John

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