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Serjik [45]
3 years ago
12

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 t

ank hold? How much water was originally in the tank? How much water is in the tank when it is 1/2 full? Please help!
Mathematics
2 answers:
ivann1987 [24]3 years ago
6 0

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 .

chubhunter [2.5K]3 years ago
5 0

Answer(s):

1.) 56 gallons

2.) 7 gallons

3.) 28 gallons

Step-by-step explanation:

<u><em>Q1: How much water can the tank hold?</em></u>

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.

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

<u><em>Q2: How much water was originally in the tank?</em></u>

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

<u><em>This means that the tank was originally 7 gallons full.</em></u> [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.]

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

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

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

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