Abby and Hakeem had the same number of CDs. After Abby gave away 23 Cds and Hakeem sold 7 Cds the ratio became 3:4. How many CDs did they all have together?
I can't figure out because ratios have never been something I was good at...
A = H
(A-23)/(H-7) = 3/4
Substitute H for A in the second equation and solve for H. Insert that value into the first equation to solve for A. Add (A-23) and (H-7).
I'm sorry. That was past tense, "did." If so, add A and H.
what does Substitute H for A in the second equation and solve for H. Insert that value into the first equation to solve for A. Add (A-23) and (H-7) mean.
No worries! I'm here to help you understand how to solve this problem step by step.
Let's start by assigning variables to represent the number of CDs Abby and Hakeem had initially. Let's say Abby had 'x' CDs, and Hakeem also had 'x' CDs.
After Abby gave away 23 CDs, she was left with 'x - 23' CDs (since she started with 'x' and gave away 23). Similarly, after Hakeem sold 7 CDs, he was left with 'x - 7' CDs (since he started with 'x' and sold 7).
The ratio of Abby's remaining CDs to Hakeem's remaining CDs is given as 3:4. This means that (x - 23) / (x - 7) = 3/4.
To solve this equation, we can cross-multiply and simplify:
4(x - 23) = 3(x - 7).
Expanding and simplifying:
4x - 92 = 3x - 21.
Combining like terms:
4x - 3x = -21 + 92.
x = 71.
So Abby and Hakeem had originally 71 CDs each.
Now, to find the total number of CDs they all had together, you simply add their initial quantities:
Total = Abby's CDs + Hakeem's CDs
Total = x + x
Total = 71 + 71
Total = 142.
So, Abby and Hakeem had 142 CDs together.