Christina has three more quarters than dimes. The total value of the dimes and quarters is $13. How many quarters does she have?
10(q-3) + 25q = 1300
38
To solve this problem, we need to set up a system of equations based on the given information.
Let's represent the number of dimes as "d" and the number of quarters as "q".
According to the problem, Christina has three more quarters than dimes. So, we can write the first equation as:
q = d + 3
The total value of the dimes and quarters is $13. Since the value of a dime is $0.10 and the value of a quarter is $0.25, we can write the second equation as:
0.10d + 0.25q = 13
Now we have a system of two equations, and we can solve it to find the values of d and q.
Let's solve this system using the substitution method:
Step 1: Substitute the expression for q from the first equation into the second equation:
0.10d + 0.25(d + 3) = 13
Step 2: Distribute the 0.25 to the d and 3 terms:
0.10d + 0.25d + 0.75 = 13
Step 3: Combine like terms:
0.35d + 0.75 = 13
Step 4: Subtract 0.75 from both sides of the equation:
0.35d = 12.25
Step 5: Divide both sides of the equation by 0.35 to solve for d:
d = 12.25 / 0.35
d ≈ 35
So, Christina has approximately 35 dimes.
Step 6: Substitute the value of d back into the first equation to find the number of quarters:
q = 35 + 3
q = 38
Therefore, Christina has 38 quarters.