Question

This equation shows the relationship between the amount of water (w), in liters, filled in Tank A and the number of minutes (m) it took to fill it.

w = 100 + 80.5m


This table shows the relationship between the amount of water, in liters, filled in Tank B and the number of minutes it took to fill the tank


Amount of water filled in Tank B:

Minutes: Amount of water: (liters)

0 154

2 384

6 844


What is the difference, in liters, between the total amount of water filled in Tank A and Tank B after 4 minutes?

Answer 1

Find equation for tank B

• (0,154)
• (2,384)

Slope:-

• m=384-154/2=230/2=115

Equation in point slope form

• w-154=115(m)
• w=115m+154

For tank B

• w=100+80.5m

Put 4on both

Tank A:-

• w=100+80.5(4)
• w=100+322
• w=422L

TankB

• w=115(4)+154
• w=460+154
• w=614L

Difference:-

• 614-422
• 192L

Answer 2

192 liters

Explanation:

Tank A

w = 100 + 80.5m

where:

• w = water in liters
• m = time in minutes

Therefore, when m = 4:

⇒ w = 100 + 80.5(4) = 422 liters

Tank B

Given ordered pairs: (0, 154) (2, 384) (6, 844)

`\sf slope\:(m)=(change\:in\:y)/(change\:in\:x)=(384-154)/(2-0)=115`

Point-slope form of linear equation:
`\sf y-y_1=m(x-x_1)`

(where m is the slope and (x₁, y₁) is a point on the line)

`\sf \implies y-154=115(x-0)`

`\sf \implies y=115x+154`

Therefore, the equation for Tank B is:

w = 115m + 154

Therefore, when m = 4:

⇒ w = 115(4) + 154 = 614 liters

Difference

614 - 422 = 192 liters