Question

Help me!! A water tank is 1/8 full. The tank is 3/4 full when 42 gallons of water is added to the tank. How much can the water tank hold? How much water was originally in the tank? How much water is in the tank when it is 1/2 full? Please help!

Answer 1

Answer(s):

1.) 56 gallons

2.) 7 gallons

3.) 28 gallons

Step-by-step explanation:

Q1: How much water can the tank hold?

Based on the question, we know that 3/4 of the tank equals 42 gallons. Divide 42 by the numerator, 3.

42/3 = 14

Now, multiply 14 by the denominator, 4.

14 x 4 = 56.

So, the tank can hold 56 gallons. [If you'd like to double check this answer, take the fraction 42/56 and simplify it to get 3/4.

Q2: How much water was originally in the tank?

We know that the tank's maximum capacity is 56 gallons. So, if it was 1/8 originally full, multiply 56 by 1/8. [Remember that 56 as a fraction can be written as 56/1]

1/8(56/1) = 7

This means that the tank was originally 7 gallons full. [If you'd like to double check this answer, take the fraction 1/8 and multiply the numerator and denominator by 7. This gets you 7/56, or 7 gallons out of the total capacity, 56 gallons.]

Q3: How much water is in the tank when it is 1/2 full?

Earlier, we found out that the maximum capacity of the tank is 56 gallons. To find out how many gallons it holds when its half full, divide 56 by 2.

56/2 = 28

So, when the tank is 1/2 full, it contains 28 gallons. [If you want to double check this answer, take  the fraction 28/56 and simplify it. When you do, you get 1/2.]

Answer 2

Answer:

The water tank holds 67.2 gallons, amount of water originally in the tank is 8.4 gallons and amount of water in the tank when it is 1/2 full is 33.6 gallons

Step-by-step explanation:

Let x be the capacity of tank .

Amount of water in tank = $\frac{1}{8}x$

Now 42 gallons water is added to tank so, tank becomes 3/4 full of water .

$\Rightarrow \frac{1}{8}x+42=\frac{3}{4}x$

$\Rightarrow 42=\frac{3}{4}x-\frac{1}{8}x$

$\Rightarrow 42=\frac{5}{8}x$

$\Rightarrow \frac{42 \times 8}{5}=x$

$\Rightarrow 67.2 =x$

So, the water tank holds 67.2 gallons .

A water tank is 1/8 full

So, amount of water originally in the tank is $\frac{1}{8} \times 67.2 = 8.4 gallons$

Amount of water in the tank when it is 1/2 full =  $\frac{1}{2} \times 67.2 = 33.6 gallons$

Hence the water tank holds 67.2 gallons, amount of water originally in the tank is 8.4 gallons and amount of water in the tank when it is 1/2 full is 33.6 gallons .