Question

There are nickels and quarters worth $2.20 in total. If there are 28 coins, how many nickels are there?

Answer 1

To solve this problem, we have to express the information we are given mathematically.

Let x be the number of nickels and y be the number of quarters. Then, the second piece of information can be stated as
x + y = 28,
since the sum of the number of coins is 28.

Now, our first piece of information is that the sum of all the nickels and quarters is $2.20 in total. We know that one quarter is worth $0.25 and a nickel is worth $0.05, so this yields that the number of nickels times the value of one nickel + the number of quarters times the value of one quarter = $2.20. Converting this to math language yields
0.05*x + 0.25*y = 2.20.

Hence, we have two equations and two unknowns. One way to solve the two equations is to solve the equation x + y = 28 for x and replace x in the second equation with
x = 28 - y.
Then you end up with an equation only in terms of y and you can solve for y. Remember that y is simply the number of quarters, so then you have solved half the problem. You should now be able to find x yourself.