1. ## Changing ratios

The number of stamps the Kaye and Alberto had were in the ratio 5:3, respectively. After Kaye gave Alberto 10 of her stamps, the ratio of the number of stamps Kaye had to the number Alberto had was 7:5. As a result of this gift, Kaye had how many more stamps than Alberto?

2. Originally Posted by mtylerrose

The number of stamps the Kaye and Alberto had were in the ratio 5:3, respectively. After Kaye gave Alberto 10 of her stamps, the ratio of the number of stamps Kaye had to the number Alberto had was 7:5. As a result of this gift, Kaye had how many more stamps than Alberto?
How far did you get? Are you able to set up an equation and then solve it?

3. I researched ratios further, and I think I just got it!

It's helpful to find the total number of stamps between them and then find their respective share post gift.

I see that Kaye's share post gift is 5/8 of the total minus 10 equals 7/12 of the total, or 5x/8 - 10 = 7x/5. Solving for x, the total number of stamps is 240. Returning to the post gift ratio, Kaye has 7/12 x 240 = 140 stamps and Alberto has 5/12 x 240 = 100 stamps. The difference between the two is 40. Kaye has 40 more stamps than Alberto after she gave him 10.

4. Originally Posted by mtylerrose
I researched ratios further, and I think I just got it!

It's helpful to find the total number of stamps between them and then find their respective share post gift.

I see that Kaye's share post gift is 5/8 of the total minus 10 equals 7/12 of the total, or 5x/8 - 10 = 7x/5. Solving for x, the total number of stamps is 240. Returning to the post gift ratio, Kaye has 7/12 x 240 = 140 stamps and Alberto has 5/12 x 240 = 100 stamps. The difference between the two is 40. Kaye has 40 more stamps than Alberto after she gave him 10.
The next step is to check your assumed answer. If it checks out, then you have solved the problem.