I have got three more dimes than quarters. The total value of my change is $2.75. How many of each coin have I got?
q+ 3 = d
.25q + .10d = 2.75
.25q + .10(q + 3) = 2.75
The above is a substitution.
If you don't like working with decimals, multiply through by 100
25q + 10(q+3) =275
35q + 10q + 30 = 275
Can you finish from here?
Ok ty
To solve this problem, we need to set up a system of equations.
Let's assume the number of quarters you have is represented by "q" and the number of dimes you have is represented by "d".
According to the information given, you have three more dimes than quarters, so we can write one equation as:
d = q + 3
The value of each quarter is $0.25, so the total value of the quarters can be represented as 0.25q.
Similarly, the value of each dime is $0.10, so the total value of the dimes can be represented as 0.10d.
We know that the total value of your change is $2.75, so we can write another equation as:
0.25q + 0.10d = 2.75
Now we have a system of equations:
d = q + 3
0.25q + 0.10d = 2.75
To solve this system, we can substitute the first equation into the second equation:
0.25q + 0.10(q + 3) = 2.75
Simplifying this equation, we get:
0.25q + 0.10q + 0.30 = 2.75
0.35q + 0.30 = 2.75
0.35q = 2.75 - 0.30
0.35q = 2.45
Dividing both sides of the equation by 0.35, we get:
q = 2.45 / 0.35
q ≈ 7
Now we know that you have 7 quarters. Substituting this value back into the first equation to find the number of dimes, we have:
d = 7 + 3
d = 10
Therefore, you have 7 quarters and 10 dimes.