Question

A collection of dimes and nickels is worth $0.55. There are 7 coins in all. How many dimes and how many nickels are there?

Answer 1

This could easily be done with just a few trial and error calculations.
However, here's how to do it using simultaneous equations.
A) D + N = 7 (meaning #dimes + #nickels is 7)
B) .1 D + .05 N = .55

Multiply equation B by -10 then add it to A
B) -1 D - .5 N = -5.50
A) D + N = 7

.5 N = 1.50
N = 3
There are 3 nickels so there are 4 dimes

3 nickels and 4 dimes have a value of .55 so we know our calculations are correct.