Question

The gauge of an oil tank indicates that it was 1/7 full. After 240 gallons were added, the gauge indicated that the tank was now 4/7 full. How many gallons does the tank hold? (Assuming that the gauge is accurate.)

Here's the solution: Start with 3 is to 7 as 240 is to full. That is because we increased the volume by 37 from 1/7 to get to 4/7 by adding 240 gallons.




How much would remain to be filled if we had added only 160 gallons when the tank was 3/7 full?

We would add _______ gallons.

Answer 1

Wow, that seems like a lot for you to try to keep up with but I'll post the solution anyway.

Answer 2

First of all, I'm not impressed with the way the given solution was presented. Here's my approach:

Let x = amount of full tank

\[\frac{x}{7} + 240 = \frac{4x}{7}\]

\[240 = \frac{4x}{7} - \frac{x}{7}\]
\[240 = \frac{4x - x}{7}\]
\[240 = \frac{3x}{7}\]

So basically at this point we know that 240 gallons means the tank is 3/7 full so that's where the 3/7 comes from. But anyway, solving for x:

\[240 \times 7 = 3x\]
\[80 \times 7 = x\]
\[560 = x\]

So the tank is full @ 560 gallons.

Answer 3

Now the second part says assume that the tank is already 3/7 full. In order words, assume that the tank already has 240 gallons. How many gallons would need to be filled if we added 160 gallons to that?

Answer 4

Well obviously 240 + 160 = 400 Gallons, therefore 560 - 400 = 160

So to fill the tank you would add 160 more gallons.

Answer 5

Any questions?

Answer 6

no thank you !

Answer 7

Did you understand any of that?