i have 17 coins nickels and dimes and a total of $1.20 how amny nickels and how many dimes?

Answer 1

First, recognize that 5 cents make a nickel, and 10 cents make a dime.

The question states that the total 17 nickels and dimes make $1.20, which when converted to cents is 120 cents.

Therefore:

nickels = n

dimes = d

Equation 1: total number of coins: n + d = 17

Equation 2: total amount of money: 5n + 10d = 120

write d in terms of n: d = 17- n; use this in Equation 2

Substituted Equation 2:

5n + 10 (17- n) = 120

5n + 170 - 10n = 120

-5n + 170 = 120

-5n = - 50

*negatives cancel out*

5n = 50

n = 10; we have 10 nickels

Back to Equation 1:

n + d = 17

10 + d = 17

d = 17 - 10 = 7; we have 7 dimes

Therefore, there are 10 nickels and 7 dimes