Question

You have four more nickels than dimes, altogether worth 95 cents.
What is x and what is y.
What are the TWO equations?
I tried this but my teacher marked me wrong so I need to know it.
Thx

Answer 1

x and y are whatever YOU define them as.

For this question, using 2 variables is more difficult than using just one

I would let x be the number of dimes.
then the number of nickels is x+4 (it said so)

Now form your equation using the value of those coins

10x + 5(x+4) = 95
15x + 20 = 95
15x = 75
x = 5
So you have 5 dimes and 9 nickels

Using 2 variables:
let the number of dimes be x
let the number of nickels be y

There are 4 more nickels than dimes
y - x = 4
or
y = x+4

for value:
10x + 5y = 95
10x + 5(x+4) = 95 ---> notice I have the same equation as I did when I used one variable
so the solution is the same steps
...
x = 5, then y = x+4 = 5+4 = 9

or

let the number of nickels be x
let the number of dimes by y
x-y = 4 ----> x = y+4

value:
5x + 10y = 95
5(y+4) + 10y = 95
5y+20 + 10y = 95
15y = 75
y = 5 , then x = 4+5 = 9
but this time x was defined as nickels
and y was defined as dimes, so
5 dimes and 9 nickels, just as before