Answer:
18 dimes, 12 quarters
Step-by-step explanation:
We are to solve the system of linear equations for D and Q, where D is the number of dimes and Q is the number of quarters.
Each dime is worth $0.10 and each quarter $0.25. Thus, D dimes are worth ($0.25/dime)D and Q quarters ($0.25/quarter)Q.
The sum of D and Q comes out to 30 coins, a mixture of dimes and quarters: D + Q = 30, so Q = 30 - D.
Now let's solve this equation: ($0.10/dime)D + ($0.25/quarter)Q = $4.80.
Substitute 30 - D for Q:
($0.10/dime)D + ($0.25/quarter)(30 - D) = $4.80
This is now entirely in D (no Q shows up). Performing the indicated multiplication, we get 0.10D + 0.25(30) - 0.25D = 4.80
Combining like terms: 0.10D - 0.25D = -0.15D, and -7.5 + 4.80 = -2.7
Thus, -0.15D = -2.70, and so D = 2.70/0.15 = 18 (There are 18 dimes.)
Since Q = 30 - D, and D - 18, Q = 30 - 18 = 12 (There are 12 quarters)
