# How many of each coin does Nadia have if she empties her purse and finds that it contains only nickels and dimes, has a total of 7 coins and they have a combined value of 55 cents?

##### 1 Answer

Oct 24, 2014

You can solve this by creating a pattern of 7 coin combinations which would include

1 dime + 6 nickels = 40 cents

2 dimes + 5 nickels = 45 cents

3 dimes + 4 nickels = 50 cents

**4 dimes + 3 nickels = 55 cents**

5 dimes + 2 nickels = 60 cents

6 dimes + 1 nickel = 65 cents

Or you could solve algebraically

Nickels are worth .05 cents

Dimes are worth .10 cents

Value of Nickels = .05 n

Value of Dimes = .10(7 - n)

Total Value = .55 cents

Algebraic Expression

.05 n + .10(7 - n) = .55

.05 n + .70 - .10 n = .55

-.05 n = .55 - .70

-.05 n = -.15

n =

n = 3 Nickels = 3

7 - 3 = 4 Dimes = 4