Complete Question
Mark has 42 coins consisting of dimes and quarters. the total value of his coins is $6. How many of each type of coin does he have?
Answer:
The number of dimes = d = 30 dimes
The number of quarters = q = 12 quarters
Explanation:
Let us represent
The number of dimes = d
The number of quarters = q
A dime is worth 10 cents = 0.10d
A quarter is worth 25 cents = 0.25q
Mark has 42 coins consisting of dimes and quarters.
q + d = 42...... Equation 1
q = 42 - d
The total value of his coins is $6.
0.1d + 0.25q = 6
We substitute 42 - d for q
0.1d + 0.25(42 - d) = 6
0.1d + 10.5 - 0.25d = 6
10.5 - 6 = 0.25d - 0.1d
4.5 = 0.15d
d = 4.5/0.15
d = 30 dimes
Solving for q
q = 42 - d
q = 42 - 30
q = 12 dimes
Therefore,
The number of dimes = d = 30 dimes
The number of quarters = q = 12 quarters