Question

Abby and Hakeem had the same number of CDs. After Abby gave away 28 CDs and Hakeem sold 17 CDs, the ratio of the number of Abby's CDs to the number of Hakeem's CDs became 2:3. How many CDs did they have altogether in the beginning?

Answer 1

In the beginning, they both has 82 CDs

Ratio is used to show the relationship that exists between numbers.  

• Let x represent the number of CDs that Abby and Hakeem had initially
• After giving out 28 CDs, the number of CDs Abby would have left is : x - 28
• After giving out 17 CDs, the number of CDs Hakeem would have left is : x - 17
• The ratio of the number of Abby's CDs to the number of Hakeem's CDs: 2 : 3

The above information can be summarised using this formula:

$\frac{x - 28}{x - 17} = \frac{2}{3}$

Cross multiply

3(x - 28) = 2(x - 17)

expand the bracket

3x - 84 = 2x - 34

combine similar terms

3x - 2x = 84 - 43

x = 41

They each had 41 CDs

Number of CDs they had together = 41 x 2 = 82

To learn more about ratios, please check: https://brainly.com/question/13419595?referrer=searchResults