A tank is two thirds full. After drawing off 100 litres of water , it is just one quarter full. what is the capacity of the tank
Solution
Let x be the capacity of the tank or the amount of water when the tank is full.
Here is how to solve this problem:
Amount of water in the tank now - 100 = amount of water left after removing 100
Since the tank is 2/3 full, the amount of water in the tank now is 2/3 times x
or 2x/3
Amount of water left after removing 100 is 1/4 times x or x/4
We them get this equation
2x/3 - 100 = x/4
2x/3 -100 + 100 = x/4 + 100
2x/3 = x/4 + 100
2x/3 - x/4 = x/4 - x/4 + 100
2x/3 - x/4 = 100
(2x × 4) / (3 × 4) - (x × 3) / (4 × 3) = 100
8x/12 - 3x/12 = 100
(8x - 3x) / 12 = 100
5x / 12 = 100
Multiply both sides by 12
(5x × 12) / 12 = 100 × 12
5x = 1200
Divide both sides by 5
5x/5 = 1200/5
x = 240
the capacity of the tank is 240 liters.
Indeed, 2/3 of 240 = (2 × 240)/ 3 = 480 / 3 = 160
160 - 100 = 60
And 60 is 1/4 of 240
Sep 11, 17 05:06 PM
Easy to follow solution to 100 hard word problems in algebra
New math lessons
Your email is safe with us. We will only use it to inform you about new math lessons.