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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.

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

Step-by-step explanation:

Let's call [tex]c[/tex] cylinders and [tex]p[/tex] prisms.

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

[tex]4c+5p=32[/tex]

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

[tex]c+8p=35[/tex]

To solve this sytem of equation, we isolate [tex]c[/tex] in the second equation

[tex]c=35-8p[/tex]

Then, we substitute this into the first equation and solve for [tex]p[/tex]

[tex]4c+5p=32\\4(35-8p)+5p=32\\140-32p+5p=32\\-27p=32-140\\p=\frac{-108}{-27}\\ p=4[/tex]

Then, we use this value to find the other one

[tex]c+8p=35\\c+8(4)=35\\c+32=35\\c=35-32\\c=3[/tex]

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

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