Mr. Winter bought four packages of ground beef. The second package weighed three times as much as the first, and the third package weighed half as much as the second. The fourth package weighed fifteen ounces, which was three ounces more than the third package. How many ounces of meat did Mr. Winter buy?

Solve algebraically.

1st package --- x

2nd package -- 3x
3rd package -- 3x/2

4th: 3x/2 + 3 = 15
3x + 6 = 30
3x = 24
x=8

1st : 8
2nd : 24
3rd : 12
4th :15
Add them up.

check :
is 15 equal to 3 more than 12 ? YES

Thank you so much!

To solve this problem algebraically, let's assign variables to the unknowns. Let's call the weight of the first package "x" ounces.

According to the given information:
- The weight of the second package is three times the weight of the first package, so it is 3x ounces.
- The weight of the third package is half the weight of the second package, so it is (1/2)(3x) = (3/2)x ounces.
- The weight of the fourth package is three ounces more than the third package, so it is (3/2)x + 3 ounces.

We need to find the total weight of all four packages, which is the sum of their weights. So the expression for the total weight is:
x + 3x + (3/2)x + ((3/2)x + 3)

Simplifying the expression:
x + 3x + (3/2)x + (3/2)x + 3

Combining like terms:
1x + 3x + (3/2)x + (3/2)x + 3
= (1 + 3 + 3/2 + 3/2)x + 3
= (7 + (3/2) + (3/2))x + 3
= (7 + 6/2)x + 3
= (7 + 3)x + 3
= 10x + 3

Therefore, the total weight of all four packages is 10x + 3 ounces. In order to find the specific value in ounces, we need to know the weight of the first package "x" in ounces.