Ratio And fraction problems

Question

Tina and Kirby had a total of 90 fish. Tina gave 1/4 of her fish to Kirby. He then gave 2/5 of his total number of fish to Tina. Then they had the same number of fish. How many did each child have at first?

please give some working out answer too.., thanks in advance.

Answer 1

Since the two of them had a total of 90 fish, let's say that Tina had x number of fish, and Kirby had (90 - x) fish.

 

If Tina gave 1/4 of her fish to Kirby, then she now has 3/4 x fish, because x - 1/4 x = 3/4 x. That means that Kirby now has (90 - x) + 1/4 x fish = 90 - 3/4 x fish.

 

Now, once Kirby gives 2/5 of his fish to Tina, he now has 3/5 of what he previously had, or:

 

3/5 * (90 - 3/4 x)

 

On the other hand, Tina now has 3/4 x + 2/5 * (90 - 3/4 x).

 

At this point, the two are supposed to have the same number of fish. Therefore, we set:

 

3/4 x + 2/5 * (90 - 3/4 x) = 3/5 * (90 - 3/4 x)

 

We need to solve this equation for x. I would begin by multiplying both sides of the equation by the LCD, which is 20. That would give us:

 

15x + 8(90 - 3/4 x) = 12(90 - 3/4 x)

 

You should now be able to solve this equation for x, Natalie.