Jake has $2.80 in dimes and quarters. he has 7 more dimes than quarters. how many quarters does he have?
10(q+7) + 25q = 280
Thank you
To solve this problem, we can set up a system of equations. Let's define the number of quarters as 'q' and the number of dimes as 'd'.
According to the problem, Jake has 7 more dimes than quarters, so we can write the equation: d = q + 7
The value of the quarters is calculated by multiplying the number of quarters by 25 cents: 25q
Similarly, the value of the dimes is calculated by multiplying the number of dimes by 10 cents: 10d
We know that the total value of the coins is $2.80, so we can write the equation: 25q + 10d = 280 cents
Now we have a system of equations:
d = q + 7 (Equation 1)
25q + 10d = 280 (Equation 2)
To solve this system, we can substitute Equation 1 into Equation 2:
25q + 10(q + 7) = 280
25q + 10q + 70 = 280
35q + 70 = 280
Subtract 70 from both sides:
35q = 210
Divide both sides by 35:
q = 6
So, Jake has 6 quarters.