Answer:
1 prism weighs 4 ounces and 1 cylinder weighs 3 ounces.
Step-by-step 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 \(p\)
\(4c+5p=32\\4(35-8p)+5p=32\\140-32p+5p=32\\-27p=32-140\\p=\frac{-108}{-27}\\ p=4\)
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.
