Tanner has $6.25 in nickels and quarters. Suppose he has 11 more nickels than quarters. How many of each coin does he have?

Question

Tanner has $6.25 in nickels and quarters. Suppose he has 11 more nickels than quarters. How many of each coin does he have?

Answer 1

These were my favorite type of problems growing up because you can treat it like a puzzle!

 

So we know that Tanner has some number of nickels (n) and some number of quarters (q).

We know that he has 11 more nickels than quarters --> n=q+11  (more implies addition, always to whichever he has less of).

We also know that the total value is $6.25.  The total value of his nickels is .05*n (since each nickel is worth 5 cents or $0.05) and the total value of his quarters is .25*q (for the same reasoning.Therefore $6.25=$0.05*n+$0.25*q.

 

Now we need to substitute q+11 for n since we know n is equal to q+11.

 

So $6.25=$0.05*(q+11)+$0.25*q.

 

Solve this equation for q, the number of quarters.  Once you have q, go back to n=q+11 to find the number of nickels.

 

Hope this helps!