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?
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
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.
I get it. Thanks guys!
To solve this problem, we need to set up two equations based on the given information. Let's represent the number of nickels by 'n' and the number of dimes by 'd'.
The first equation is based on the total number of coins:
n + d = 22
The second equation is based on the total value of her change:
0.05n + 0.10d = 1.75
Here's how we arrived at the second equation:
- The value of a nickel is $0.05, so the value of 'n' nickels is 0.05n.
- Similarly, the value of a dime is $0.10, so the value of 'd' dimes is 0.10d.
- The sum of these values must equal $1.75, as given.
Now we can solve these equations simultaneously to find the values of 'n' and 'd'.