A girl has been getting her parents change every day for a year. She has dimes and half-dollars worth $30.00. If she has five times as many dimes as half-dollars, how many of each type of coin does she have?
d + h = 3000
d = 5 h
solve the system ... substitution looks good
update
10 d + 50 h = 3000
d = 5 h
solve the system ... substitution looks good
To solve this problem, let's assign variables to the unknowns. Let:
- x be the number of half-dollars the girl has,
- 5x be the number of dimes the girl has.
Now, we can set up an equation to represent the scenario given in the problem. The value of the half-dollars is equal to the value of the dimes:
0.5x + 0.10(5x) = 30.00
Let's solve the equation:
0.5x + 0.50x = 30.00
0.60x = 30.00
x = 30.00 / 0.60
x ≈ 50
Therefore, the girl has 50 half-dollars (0.5 * 50 = $25) and 5 times as many dimes, or 250 dimes (0.10 * 250 = $25).