Question

Write a system of equations to describe the situation below, solve using substitution, and fillin the blanksCora works in the shipping department of a toy factory that makes radio-controlledhelicopters. Small helicopters weigh 1 kilogram each, and are shipped in a container thatweighs 8 kilograms. Large ones, on the other hand, weigh 2 kilograms apiece, and areshipped in a container that weighs 5 kilograms. If these boxes can hold a certain number ofhelicopters each, all of the packed containers will have the same shipping weight. What wouldthe total weight be? How many helicopters would fit in either container?

Answer 1

Step 1:

In this question, we are given the following:

Cora works in the shipping department of a toy factory that makes radio-controlled helicopters.

Small helicopters weigh 1 kilogram each, and are shipped in a container that

weighs 8 kilograms:

`\text{x+ 8}`

Large ones, on the other hand, weigh 2 kilograms a piece, and are shipped in a container that weighs 5 kilograms:

`2x\text{ + 5}`

If these boxes can hold a certain number of helicopters each, all of the packed containers will have the same shipping weight.

`\begin{gathered} This\text{ means that:} \\ \text{x + 8 = 2 x + 5} \\ collect\text{ing like terms, we have that:} \\ 8-\text{ 5 = 2 x - x} \\ x\text{ = 3} \end{gathered}`

PART ONE:

What would the total weight be?

`\begin{gathered} The\text{ total weight = 11 kg} \\ since\text{ } \\ from\text{ x = 3} \\ x+\text{ 8 = 3 + 8 = 11 kg} \\ and \\ from\text{ 2 x+ 5,} \\ 2(3)\text{ + 5 = 6 + 5 = 11 kg} \end{gathered}`

PART TWO:

How many helicopters would fit in either container?

`\begin{gathered} Let\text{ the numbr of helicopters be x,} \\ Then \\ \text{ x+ 8 = 2 x+ 5} \\ collecting\text{ like terms, we have that:} \\ 2x\text{ - x = 8 - 5} \\ \text{x = 3} \\ Hence,\text{ number of helicopters = 3} \end{gathered}`