Question

you have a bottle of water with a leak. after 2 seconds there is 28 ounces left in the bottle. after 6 seconds there are 20 ounces left in the bottle. how much water was in the bottle initially

Answer 1

Answer: 32 ounces.

Step-by-step explanation:

We can think of this as a linear equation.

y = a*x + b

where y is the amount of water in the bottle, a is the rate at which loses water, x is the number of seconds and b is the initial amount of water.

We have two pairs:

2 seconds - 28 ounces left or (2, 28)

6 seconds - 20 ounces left or (6, 20)

Now we can write the value of a as:

a = (20 - 28)/( 6 - 2) = -8/4 = -2 ounces per second.

Then our function is:

y = -2x + b

and we know that when x = 2, y = 28, so we have:

28 = -2*2 + b = -4 + b

b = 28 + 4 = 32

the initial amount of water in the bottle is 32 ounces.

Answer 2

Between the 2 second mark and 6 second mark, 4 seconds passed and 8 ounces leaked out.
8 ÷ 4 = 2, the ounces per second leaking. 
Multiply it by 2 to get 4, the amount leaked after 2 seconds. 
Add 4 to 28 to get 32 ounces, the initial amount. 
Hope this helps!