Question

The scatter graph shows some information about badge stalls at a festival.

Use the line of best fit to estimate the number of hours that a stall was open for
if it had 160 badges left to sell.
Number of badges left
Badge stalls and how long they were open for
300
200
100
6
Number of hours open
10
12

Answer 1

We used a step-by-step approach to solve the linear equation 4 + 2x = 160, which involved rearranging the terms, subtracting a constant term from both sides, and dividing both sides by a common factor. This allowed us to isolate x and find that the stall was open for approximately 78 hours if it had 160 badges left to sell.

Let's estimate the number of hours a stall was open for if it had 160 badges left to sell, based on the information in the scatter plot.

Step 1: Rearrange the terms

The equation in the image is given as 4 + 2x = 160. We need to manipulate this equation to isolate x, which represents the number of hours the stall was open. To do this, we'll start by rearranging the terms so that all the x terms are on one side of the equation:

2x + 4 = 160

Step 2: Subtract 4 from both sides

To isolate x further, we need to get rid of the constant term on the left side of the equation. We can do this by subtracting 4 from both sides of the equation:

2x + 4 - 4 = 160 - 4

This simplifies to:

2x = 156

Step 3: Divide both sides by 2

Now, we need to isolate x by itself. To do this, we can divide both sides of the equation by 2:

(2x) / 2 = (156) / 2

This simplifies to:

x = 78

Therefore, based on the information in the scatter plot, the stall was open for approximately 78 hours if it had 160 badges left to sell.