Tim has three more dimes than quarters and 6 fewer nickeles than quarters. I he has 63 coins toal than how many quarters does Tim have.

Question

I dont know how to do this. I have to write an algebraic equation.

Answer 1

For problems like this one, it's best to break it up into simpler steps and put it back together

First, lets define variables for each coin:

d = # of dimes
n = # of nickels
q = # of quarters

From what is given:
"three more dimes than quarters" -> The number of dimes equals the number of quarters plus 3 more:
d = q + 3

"6 fewer nickels than quarters" -> The number of nickels equals the number of quarters minus 6
n = q - 6

Now we have everything in terms of q:
d = q + 3
n = q - 6
q = q (the value of q didn't change).

Lets say:
t = total number of coins

therefore:
t = d + n + q

Substituting d and n:
t = (q + 3) + (q - 6) + q
t = 3*q - 3

so, if t = 63

3*q - 3 = 63
3*q = 66
q = 22