Question

Beatrice is weighing combinations of geometric solids. she found that 4 cylinders and 5 prisms weigh 32 ounces and that 1 cylinder and 8 prisms weigh 35 ounces. write and solve a system of equations to determine the weight of each cylinder and prism.

Answer 1

1 prism weighs 4 ounces and 1 cylinder weighs 3 ounces.

Explanation:

Let's call
`c` cylinders and
`p` prisms.

Now, if 4 cylinders and 5 prisms weigh 32 ounces, that can be expressed as

`4c+5p=32`

Also, 1 cylinder and 8 prisms weigh 35 ounces, so

`c+8p=35`

To solve this sytem of equation, we isolate
`c` in the second equation

`c=35-8p`

Then, we substitute this into the first equation and solve for
`p`

`4c+5p=32\\4(35-8p)+5p=32\\140-32p+5p=32\\-27p=32-140\\p=(-108)/(-27)\\ p=4`

Then, we use this value to find the other one

`c+8p=35\\c+8(4)=35\\c+32=35\\c=35-32\\c=3`

Therefore, 1 prism weighs 4 ounces and 1 cylinder weighs 3 ounces.