This is a math problem that involves solving a system of equations. To find the total amount that you spend on ham and cheese, we need to find the values of x and y, where x is the number of pounds of ham that you asked for, and y is the number of pounds of cheese that you asked for.
We can use the following information to set up two equations:
- You end up getting 4 extra ounces of ham and 3 fewer ounces of cheese. This means that the actual weights of ham and cheese that you get are (x + 0.25) pounds and (y - 0.1875) pounds, respectively. (Note: 1 pound = 16 ounces)
- The ham costs $6.24 per pound and the cheese costs $4.80 per pound. This means that the cost of ham per ounce is $0.39, and the cost of cheese per ounce is $0.30.
- You spend twice as much on ham as you do on cheese. This means that the total cost of ham is equal to two times the total cost of cheese.
Using these facts, we can write the equations as follows:
- Equation 1: (x + 0.25) * 0.39 = 2 * (y - 0.1875) * 0.30
- Equation 2: x = y
We can solve these equations by substituting x with y in equation 1, and then simplifying and rearranging the terms:
- (y + 0.25) * 0.39 = 2 * (y - 0.1875) * 0.30
- 0.39y + 0.0975 = 0.6y - 0.1125
- -0.211y = -0.21
- y = 1
Then, we can plug in y = 1 in equation 2 to get x:
- x = y
- x = 1
Therefore, the values of x and y are both equal to 1, which means that you asked for one pound of ham and one pound of cheese.
To find the total amount that you spend on ham and cheese, we need to multiply the actual weights of ham and cheese by their respective costs per ounce, and then add them together:
- Total cost = ((x + 0.25) * 0.39) + ((y - 0.1875) * 0.30)
- Total cost = ((1 + 0.25) * 0.39) + ((1 - 0.1875) * 0.30)
- Total cost = (1.25 * 0.39) + (0.8125 * 0.30)
- Total cost = $0.4875 + $0.24375
- Total cost = $0.73125
Therefore, the total amount that you spend on ham and cheese is $0.73125.