To find out how many of each item Clem Colfax purchased, we can set up equations based on the given information. Let's assign variables to represent the quantities of each item:
Let's say Clem purchased:
- x cartons of milk,
- y loaves of bread,
- z boxes of cereal,
- w pounds of meat.
According to the given information, Clem bought twice as many cartons of milk as loaves of bread:
x = 2y
The number of boxes of cereal was one more than the number of loaves of bread:
z = y + 1
The number of pounds of meat was the same as the number of boxes of cereal:
w = z
Now, let's convert the prices of each item into cents for convenience:
Milk: 70 cents per carton
Bread: 60 cents per loaf
Cereal: 50 cents per box
Meat: $1.50 per pound = 150 cents per pound
The total cost of milk will be 70 * x cents.
The total cost of bread will be 60 * y cents.
The total cost of cereal will be 50 * z cents.
The total cost of meat will be 150 * w cents.
We know that the total cost is exactly $10, which is equivalent to 1000 cents:
70x + 60y + 50z + 150w = 1000
Now, let's try to solve this system of equations to find the values of x, y, z, and w.
From the equation x = 2y, we can substitute the value of x in the equation above:
70(2y) + 60y + 50z + 150w = 1000
Simplifying the equation, we get:
140y + 60y + 50z + 150w = 1000
200y + 50z + 150w = 1000
Substituting the value of z from z = y + 1:
200y + 50(y + 1) + 150w = 1000
200y + 50y + 50 + 150w = 1000
250y + 150w = 950
Since we have two variables (y and w), we cannot solve this system without additional information. It appears that the given information is incomplete or there is an error in the problem statement.
Please double-check the information provided to see if there are any missing details or errors.