Question

Write a linear model for the amount of boxes, b, as a function of the number of hours since they opened, h. Use your model to predict the number of boxes in stock at the end of an 8 hour shift.

Answer 1

Question:

A company produces boxes of DVDs at a rate of 52 boxes per hour they begin to produce boxes when they first opened for the day and after 3 hours have 400 boxes in stock.

- How many boxes were in stock when they opened?

- Write a linear model for the amount of boxes, b, as a function of the number of hours since they opened, h.

- Use your model to predict the number of boxes in stock at the end of an 8 hour shift.

Answer:

1. $Initial = 244$

2. $b = 244 + 52h$

3. 660 boxes

Step-by-step explanation:

Given

$Rate = 52\ per\ hour$

$Total\ boxes\ in\ 3\ hours = 400$

Solving (a): Initial Number of boxes

First, we calculate the number of boxes made in 3 hours

$Boxes = Rate * Hours$

$Boxes = 52 * 3$

$Boxes = 156$

If they had 400 boxes at the 3rd hour.

Then, the number of boxes when they opened is:

$Initial = 400 - 156$

$Initial = 244$

Solving (b): Linear function

$b = boxes$

$h = hours$

Since, we have the rate and the initial number of boxes.

The linear function is:

$Boxes = Initial + Rate * Hours$

i.e.

$b = 244 + 52 * h$

$b = 244 + 52h$

Solving (c): Boxes at the end of the 8th hour

We have:

$b = 244 + 52h$

In this case:

$h = 8$

Substitute 8 for h

$b = 244 + 52 * 8$

$b = 244 + 416$

$b = 660$

Hence, there are 660 boxes at the end of the 8th hour