Question

There are 2 cups of equal capacity which contain water. Cup A is 7/8 full and cup B is 2/5 full. What fraction of cup A must be poured into cup B so that the two cups will contain thesame amount of water?A) 51/40B) 19/98051/80

Answer 1

The correct answer is B)19/80

In order to have the same amount of water in each cup we can add the water of the two cups and divede by two, to know how much water we need tu pour from cup A to cup B

Let's add the water:

`(7)/(8)+(2)/(5)=(7\cdot5)/(8\cdot5)+(2\cdot8)/(5\cdot8)`

to add them we need to find equivalents fractions. In the fraction on the left I multiply by 5, because is the denominator of the fraction of the left. And with the fraction on the right I did the same thing, multiplying by 8

Then:

`(35)/(40)+(16)/(40)=(51)/(40)`

To know how much water has to be ijn each cup, divide by 2, or multiply by 1/2, it's the same.

`(51)/(40)\cdot(1)/(2)=(51)/(40)/2=(51)/(80)`

Now, the promlem asks how much we need to extract from cup A to fill cup B. This means that cup A has an amount of water grater than 51/80. To know how much is that amount, lets calculate it:

`(7)/(8)-(51)/(80)=(7\cdot10)/(8\cdot10)-(51)/(80)=(70)/(80)-(51)/(80)=(19)/(80)`

The amount of water we need to pour from cup A to cup B is 19/80, wich is option B