Question

Sophia has 22 coins in her pocket, all of which are nickels and dimes. If the total value of her change is $1.75, how many nickels and how many dimes does she have?

Im lost on how to set up the equations, please help and show me how?

Answer 1

you can use two variables:
number of nickels --- x
number of dimes ---- y

x+y = 22
5x + 10y = 175 --> divide by 5
x + 2y = 35
subtract them:
y = 13
sub back into x+y = 22 ----> y = 9

or, using one variable:

let the number of nickels be x
then the number of dimes = 22-x
5x + 10(22-x) = 175
5x + 220 - 10x = 175
-5x = -45
x = 9
22-x = 13

Answer 2

or, say she has equal amounts of coins: 11 nickels, 11 dimes. The total amount is 11*5+11*10 = 165

Yet we are told that she has 175.

Each time we replace a nickel with a dime, we get 5 more cents. So, to get those extra 10 cents, we need to replace 2 nickels with dimes:

9 nickels and 13 dimes.

Answer 3

I get it. Thanks guys!