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.
Dis is so easy.
Q+D=X
1.1Q+D=1.75X
now solve it idiots
To solve this problem, let's assume that the box originally contains x quarters and y dimes. We can then use two equations to represent the given information.
First, we are told that if there were 10% more quarters, the total value of the money in the box would increase by 7.5%. This can be expressed as the equation:
0.075 = 0.10(x + 0.10x + y) - 0.10(x + y)
Simplifying this equation, we get:
0.075 = 0.10(1.10x + y) - 0.10x - 0.10y
Now, let's consider the total value of the money in the box. The value of a quarter is 25 cents (0.25) and the value of a dime is 10 cents (0.10). Therefore, we can write the second equation:
0.25x + 0.10y = value of the money in the box
Now, we have a system of two equations:
0.075 = 0.10(1.10x + y) - 0.10x - 0.10y
0.25x + 0.10y = value of the money in the box
To solve this system, we can start by simplifying the first equation:
0.075 = 0.11x + 0.10y - 0.10x - 0.10y
0.075 = 0.01x
x = 0.01 / 0.075
Next, we can substitute this value of x into the second equation to solve for y:
0.25(0.01 / 0.075) + 0.10y = value of the money in the box
0.0025 + 0.10y = value of the money in the box
0.10y = value of the money in the box - 0.0025
Finally, to find the ratio of the number of quarters to dimes, we can divide x by y:
x/y = 0.01 / 0.10y
Therefore, the ratio of the number of quarters to dimes in the box is 0.01 / 0.10y.
(Note: To find the exact values for x and y, you would need to know the value of the money in the box and solve the equations accordingly. However, the given problem does not provide that information.)