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.
D = Q + 20
.10D + .25Q = 5.50
Substitute Q+20 for D and solve for Q. Insert Q value in first equation to find D. Put both values into the second equation to check.
To find the number of dimes and quarters Logan saves, we can set up a system of equations based on the given information.
Let's assume that Logan saves x quarters and (x + 20) dimes.
The value of x quarters can be represented as 0.25x (since each quarter is worth $0.25), and the value of (x + 20) dimes can be represented as 0.10(x + 20) (since each dime is worth $0.10).
We know that the total value of the dimes and quarters is $5.50, so we can set up the equation:
0.25x + 0.10(x + 20) = 5.50
Now we can solve this equation to find the value of x (the number of quarters):
0.25x + 0.10x + 2.00 = 5.50
0.35x + 2.00 = 5.50
0.35x = 5.50 - 2.00
0.35x = 3.50
Dividing both sides by 0.35:
x = 3.50 / 0.35
x = 10
Therefore, Logan saves 10 quarters and (10 + 20) = 30 dimes.