THREE LINEAR EQUATIONS WITH THREE VARIABLES

Question

A collection of nickels, dimes, and quarters consist of 7 coins with a total of $1.05. If the number of dimes is equal to the number of nickels, find the number of each type of coins. How do I set up this problem in three linear equations to find the answers? Please help.

Answer 1

Since # nickels = # dimes, you can solve this as a system of 2 equations with two unknowns.

 

But since n+n+q = 7, you can eliminate q because it's = to 7-2n.

 

Now you have one equation with only one unknown (n nickels)--said equation reflects the monetary value.  This will be easy for you to write & solve.