SOLUTION: A purse contains $3.45 in quarters, dimes, and nickels. It contains three fewer than three-fourths as many dimes as nickels, and two fewer quarters than dimes. How many nickels are

Question 1160588: A purse contains $3.45 in quarters, dimes, and nickels. It contains three fewer than three-fourths as many dimes as nickels, and two fewer quarters than dimes. How many nickels are in the purse?
I can not determine my first equation.
This is what I have
Nickels: x
Dimes: 3/4x-3
Quarters: (3/4x-3)-2
Do I have any of this correct and could you help me solve please
Found 2 solutions by solver91311, ikleyn:
Answer by solver91311(24713)   (Show Source): You can put this solution on YOUR website!

You are on the right track but have a little farther to go. Your three expressions are representative of the number of nickels, dimes, and quarters and are properly formed according to the parameters in the question. However, the question does not provide information on the total number of coins. It does provide the total value of the coins, so what you need to do is convert the expressions for numbers of coins to the values of the coins. When I do one of these, I generally convert values given in dollars and cents to just cents so that I eliminate having to deal with decimal coefficients in my equations.

The value of a nickel is 5 cents, so the value of nickels is cents. Similarly, the value of the dimes is cents and the value of the quarters is cents. And since the total value is $3.45 which is 345 cents, we have:

Expand the parentheticals

Collect the constant terms in the RHS

Multiply both sides by 4 to eliminate the fractions.

Collect the variable terms and divide by the resulting coefficient on

John

My calculator said it, I believe it, that settles it

Answer by ikleyn(52803)   (Show Source): You can put this solution on YOUR website!
.

To see many other similar solved problems, look into the lessons
    - Advanced word problems to solve using a single linear equation
    - HOW TO algebreze and solve these problems using one equation in one unknown
    - OVERVIEW of lessons on solving linear equations and word problems in one unknown
in this site.

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Happy learning (!)

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