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?

Answers

Reiny
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
Steve
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.
Sam
I get it. Thanks guys!

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