Question

You are riding a train. Your carry-on bag can weigh no more than 50 pounds. Your bag weighs 38 pounds. Which inequalities represent how much weight you can add to your bag?

w > 50 - 38
50 > W - 38
38 + w< 50
w< 50 - 38

Can you add both a 9-pound laptop and a 5-pound pair of boots to your bag without going over the weight limit?
Yes, the total being added is 4 pounds, which is a solution of the inequality.
No, the total being added is 14 pounds, which is not a solution to the inequality.
Yes, the added weight needs to be less than 38 pounds, and 9 plus 5 is less than 38.
No, the added weight needs to be at least 38 pounds, and 9 plus 5 is less than 38.​

Answer 1

A. The inequalities are:

`w + 38 \leq 50`

`38 + w \leq 50`

`w \leq 50 - 38`

B. No, the total being added is 14 pounds, which is not a solution to the inequality.

Explanation:

Given

`Maximum = 50`

`Bag = 38`

Solving (a): Expression that represent the possible additional weight

Represent the additional weight with w

When w is added to the weight of the bag it must not be more than 50;

Not more than means less than or equal to

This is represented by

`w + 38 \leq 50` or
`38 + w \leq 50`

Make w the subject

`w \leq 50 - 38`

Solving (b): If 9lb and 5lb is added to the bag, will it go overweight?

First, we need to solve the inequality in (a)

`w \leq 50 - 38`

`w \leq 12`

This means that additional weights must not exceed 12 pounds

Adding 9lb and 5lb, we have:

`9 + 5 = 14`

14 pounds is more than 12 pounds.

Hence: option B answers the question