Question

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?

Answer 1

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
# of Nickels = n # of Dimes = 7 - n
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 = `(-.15)/(-.05)`

n = 3 Nickels = 3
7 - 3 = 4 Dimes = 4