Mr. Scrooge bought 4 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. Scrooge buy?
Solve algebraically.
Please help me understand how to write the equation correctly, I’ve worked out the no. of ounces sold is 59 as well as how many ounces each package has
Package 4 = 15 ozs
Package 3 = 15 – 3 = 12
Package 2 = 12 x 2 = 24
Package 1 = 24 /3 = 8
To solve this problem algebraically, we need to use variables to represent the weights of the packages.
Let's say the weight of the first package is x ounces.
According to the problem, the weight of the second package is three times the weight of the first package, which can be expressed as 3x ounces.
The weight of the third package is half the weight of the second package, so it would be (1/2)(3x) = (3/2)x ounces.
Finally, we know that the weight of the fourth package is 15 ounces, which is three ounces more than the weight of the third package, so it would be (3/2)x + 3 ounces.
Now, we can write an equation to represent the total weight of all four packages:
x + 3x + (3/2)x + (3/2)x + 3 = Total weight
Simplifying the equation, we have:
8x + 3 = Total weight
Given that the total weight is 59 ounces, we can write:
8x + 3 = 59
Now, we can solve the equation for x:
8x = 59 - 3
8x = 56
x = 56 / 8
x = 7
Therefore, the weight of the first package is 7 ounces.
To find the total weight of the four packages, we substitute the value of x into the equation:
Total weight = 8x + 3
Total weight = 8(7) + 3
Total weight = 59 ounces
So, Mr. Scrooge bought 59 ounces of meat.