Hi Bellah!
This is a system of equation word problem. For these problems, we want to identify the 2 types of things and the 2 different units:
Our two things are quarters and nickels.
Our two units are cents and total coins.
From here, we can write an equation with the matching information and solve:
let q be quarters and n be nickels.
q+n= 64 (the amount of quarters plus the amount of nickels is 64 total coins)
.25q+.05n=6.60 (25 cents for every quarter plus 5 cents for every nickel will give us a total of 6.60 total cents).
We can use substitution or elimination to solve this problem. To keep it simple, I would opt for substitution.
Solve the first equation for either of the variables, as follows:
q+n=64
-q -q
_________
n=64-q
From there, substitute 64-q for n into the second equation:
.25q+.05(64-q)=6.60
I would multiply both sides of this equation by 100 to eliminate the decimals. It’s optional, but, since I teach SAT math, I love all steps that can mitigate errors! Remember to multiply both sides!
X100 (.25q+.05(64-q))=6.60(X100)
We distribute the 100 to each term, and from there, we can solve the equation decimal-free!
25q+5(64-q)=660
25q+320-5q=660
20q+320=660
-320 -320
___________
20q=340
divide both sides by 20 and get q=17
to find n, plug 17 back into the first equation: 17+n=64
subtract 17 from both sides to get n =47
Let's check to see if our values work:
47 nickels times .05 = 2.35
17 quarters times .25 = 4.25
Add these totals together, and we will get $6.60, which satisfies the problem.
Hope that helps!
