A box contains only quarters and dimes. If there 10% more quarters, the total value of the money in the box would increase by 7.5%. What is the ratio of the number of quarters and dimes in the box? Express your answer as a common fraction.
current value is 10d+25q
10d+25(1.1q) = 1.075(10d+25q)
10d + 27.5q = 10.75d + 26.875
.625q = .75d
q/d = .75/.625 = (3/4)/(5/8) = 6/5
My math is similar to person #1's. Sid is wrong, young ones. He is deeply, deeply wrong.
prolly
To solve this problem, let's assign variables to the unknowns. Let's say there are "q" quarters and "d" dimes in the box.
Since the problem tells us that if there were 10% more quarters, the total value of the money in the box would increase by 7.5%, we can set up the following equation:
(0.10q + q) + (0.10d) = 1.075(q + d)
Let's simplify this equation step by step:
0.10q + q + 0.10d = 1.075q + 1.075d
Combining like terms:
1.10q + 0.10d = 1.075q + 1.075d
Now, let's isolate the variables:
1.10q - 1.075q = 1.075d - 0.10d
0.025q = 0.975d
Dividing both sides by 0.025:
q = (0.975d) / 0.025
Simplifying:
q = 39d
Therefore, the ratio of quarters to dimes is 39:1, which can be expressed as the common fraction 39/1.