Final answer:
Using a system of equations, it is determined that the weight of each cylinder is 3 ounces and the weight of each prism is 4 ounces by setting up two equations with the given weights and solving them using elimination.
Step-by-step explanation:
The student is working on a problem involving system of equations. In this specific case, we have two equations based on the combinations of cylinders and prisms and their total weights. We can represent the weight of each cylinder as c and the weight of each prism as p.
Step 1: Set Up the Equations
From the information given, we can write two equations:
- 4c + 5p = 32 (four cylinders and five prisms weigh 32 ounces)
- 1c + 8p = 35 (one cylinder and eight prisms weigh 35 ounces)
Step 2: Solve the System of Equations
To solve these equations, we can use the method of substitution or elimination. Let's use elimination.
Multiply the second equation by 4 to balance the number of cylinders:
- 4c + 5p = 32
- (4c + 32p = 140)
Subtract the first equation from the second:
- 4c + 32p - 4c - 5p = 140 - 32
- 27p = 108
- p = 108 / 27
- p = 4 (weight of each prism)
Now, substitute p = 4 into the first equation:
- 4c + 5(4) = 32
- 4c + 20 = 32
- 4c = 12
- c = 12 / 4
- c = 3 (weight of each cylinder)
So, the weight of each cylinder is 3 ounces and the weight of each prism is 4 ounces.