a purse contains $7.45 in quarters and dimes 13 more quarters than dimes how many quarters and how many dimes are there
10D+25Q=7 45
but Q-13=D
or 10(Q-13)+25Q=7 45
or 35Q=745+130=775
Q=25
number of dimes ---- x
number of quarters ---- x+13
10x + 25(x+13) = 745
solve for x
12 dimes and 25 quarters
To solve this problem, we can use algebraic equations. Let's represent the number of dimes as "D" and the number of quarters as "Q".
According to the given information, we know that the total value of the coins is $7.45.
The value of a dime is $0.10, so the total value of dimes can be expressed as 0.10D.
Similarly, the value of a quarter is $0.25, so the total value of quarters can be expressed as 0.25Q.
Now we can create two equations based on the information given:
1. The first equation represents the total value of the coins:
0.10D + 0.25Q = 7.45
2. The second equation represents the relationship between the number of quarters and dimes:
Q = D + 13
Now we can solve the system of equations to find the values of Q and D.
Substituting the second equation into the first equation, we get:
0.10D + 0.25(D + 13) = 7.45
Simplifying the equation:
0.10D + 0.25D + 3.25 = 7.45
0.35D = 4.20
D = 12
Substituting the value of D back into the second equation:
Q = 12 + 13
Q = 25
Therefore, there are 25 quarters and 12 dimes in the purse.