Question

Isabella filled her pool with water at a constant rate.
The table compares the remaining volume of water left to fill the pool (in liters) and the time since Isabella started filling the pool (in minutes).
Time (minutes) Water (liters)
2 184
7 94
12 4
What is the size of Isabella's pool?

Answer 1

Answer:

The size of Isabella's pool is 220 liters.

Step-by-step explanation:

Let the size of Isabella's pool be $x$ liters, $R$ be the rate of fill, $t$ be the time of fill and $V$ be the volume of water filled in the pool.

As the rate of fill is constant,

Therefore, volume of water filled in the pool can be given as,

$V= Rt$

Volume of water left is given as $x-V=x-Rt$

From the table,

Volume of water left after $t=2$ minutes is 184 liters.

So, $x-R(2)=184\\x-2R=184$ -------- 1

Volume of water left after $t=12$ minutes is 4 liters.

So, $x-R(12)=4\\x-12R=4$ ------------2

Multiply equation 1 by 6 and equation 2 by -1, we get

$6x-12R=1104\\-x+12R=-4$

Now, we add the above equations, we get

$(6x-x)+(12R-12R)=1104-4\\5x=1100\\x=\frac{1100}{5}=220$

Therefore, the size of Isabella's pool is 220 liters.