Logan saves $5.50 in dimes and quarters over a week. He has 20 more dimes than quarters. Find the number of dimes and quarters he saves.
How do I solve the problem algebraically?
To solve this problem algebraically, we can set up a system of equations.
Let's say the number of quarters Logan saves is represented by q, and the number of dimes is represented by d.
According to the information given, we have two equations:
1) Logan saves $5.50 in dimes and quarters:
0.25q + 0.10d = 5.50
2) Logan has 20 more dimes than quarters:
d = q + 20
Now, we can use these equations to solve for the values of q and d.
First, substitute the value of d from equation 2 into equation 1:
0.25q + 0.10(q + 20) = 5.50
Simplify the equation:
0.25q + 0.10q + 2 = 5.50
0.35q + 2 = 5.50
Subtract 2 from both sides:
0.35q = 3.50
Divide both sides by 0.35:
q = 10
Now, substitute the value of q back into equation 2 to find the value of d:
d = 10 + 20
d = 30
Therefore, Logan saves 10 quarters and 30 dimes.