A girl has $3.35 in her pocket, consisting of dimes and quarters. If there are 23 coins in all, how many of each does she have?
quarters is 7 and dimes 16, it is right.
To solve this problem, we can set up a system of equations. Let's denote the number of dimes as 'd' and the number of quarters as 'q'.
From the given information, we know that the total value of the coins is $3.35. Since a dime is worth $0.10 and a quarter is worth $0.25, we can write the first equation as:
0.10d + 0.25q = 3.35
We also know that there are 23 coins in total, so our second equation is:
d + q = 23
Now we have a system of two equations:
0.10d + 0.25q = 3.35
d + q = 23
To solve this system, we can use substitution or elimination. Let's solve by substitution.
Rearrange the second equation to express one variable in terms of the other:
d = 23 - q
Substitute this expression for 'd' in the first equation:
0.10(23 - q) + 0.25q = 3.35
Distribute 0.10:
2.30 - 0.10q + 0.25q = 3.35
Combine like terms:
0.15q = 1.05
Divide both sides by 0.15:
q = 7
Now substitute this value back into the second equation to solve for 'd':
d + 7 = 23
Subtract 7 from both sides:
d = 16
Therefore, the girl has 16 dimes and 7 quarters.
number of quarters --- x
number of dimes -----23-x
25x + 10(23-x) = 335
solve for x