Benjamin has $7.40 in change in his pocket, all in dimes and quarters, he has 44 coins in all. How many dimes does he have?
Q = 44 - D
10D + 25Q = $7.40
Substitute 44-D for Q in the second equation and solve for D.
To find the number of dimes Benjamin has, we can set up a system of equations using the given information. Let's assign variables to the unknowns:
Let's say the number of dimes Benjamin has is represented by 'd', and the number of quarters is represented by 'q'.
From the problem, we are given two pieces of information:
1. Benjamin has 44 coins in total: d + q = 44 (Equation 1).
2. The total value of the change is $7.40: 0.10d + 0.25q = 7.40 (Equation 2).
Now, we can solve this system of equations to find the value of 'd' (the number of dimes).
We can start by isolating one of the variables in Equation 1. Let's solve for 'd':
d = 44 - q
Now, substitute this value of 'd' into Equation 2:
0.10(44 - q) + 0.25q = 7.40
Now, simplify the equation:
4.4 - 0.10q + 0.25q = 7.40
Combine the 'q' terms:
0.15q = 3
Simplify further:
q = 3 / 0.15
q = 20
So, Benjamin has 20 quarters.
Now, substitute this value of 'q' back into Equation 1 to find 'd':
d + 20 = 44
d = 44 - 20
d = 24
Therefore, Benjamin has 24 dimes in his pocket.