Annie has quarters and dimes in her bank. There are 8 less than 4 times as many dimes as quarters. There is $6.35 in her bank. How many dimes are in her bank?
To find the number of dimes in Annie's bank, we need to set up equations based on the given information.
Let's assume that Annie has q quarters and d dimes.
From the given information, we know that there are 8 less than 4 times as many dimes as quarters. Mathematically, this can be expressed as:
d = 4q - 8 (Equation 1)
We are also given that there is $6.35 in Annie's bank. The total value of the quarters and dimes can be calculated as:
Total value = (Value of quarters) + (Value of dimes)
Since a quarter is worth $0.25 and a dime is worth $0.10, we can write the equation as:
$6.35 = 0.25q + 0.10d (Equation 2)
Now we have a system of two equations (Equations 1 and 2) that we can solve to find the values of q and d.
To solve the system of equations, we can use substitution or elimination method. Let's use the substitution method:
Substitute the value of d from Equation 1 into Equation 2:
$6.35 = 0.25q + 0.10(4q - 8)
$6.35 = 0.25q + 0.40q - 0.80
Simplify the equation:
$6.35 = 0.65q - 0.80
Add 0.80 to both sides:
$7.15 = 0.65q
Divide both sides by 0.65:
q = $7.15 / 0.65
q ≈ 11
So, Annie has approximately 11 quarters in her bank.
Now, substitute the value of q back into Equation 1 to find the number of dimes:
d = 4q - 8
d = 4(11) - 8
d = 44 - 8
d = 36
Therefore, Annie has 36 dimes in her bank.
4D=Q+8
10D+25Q=635