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-23)/(h-7)=3/4
but a=h
(a-23)/(a-7)=3/4
4a-92=3a-21
a=71
check that.
together:2*a
No problem! Let's break down the problem step by step and use some algebra to solve it.
Let's start by assigning variables to the unknown quantities. Let's say Abby and Hakeem each started with x number of CDs. This means that after Abby gave away 23 CDs, she was left with (x - 23) CDs. Similarly, Hakeem sold 7 CDs, so he was left with (x - 7) CDs.
Now, we know that the ratio of the number of CDs Abby had to the number of CDs Hakeem had is 3:4. This can be written as:
(x - 23) / (x - 7) = 3/4
To solve this equation, we can cross-multiply:
4(x - 23) = 3(x - 7)
Simplifying this equation:
4x - 92 = 3x - 21
Moving all the variables to one side:
4x - 3x = -21 + 92
x = 71
Now that we know x, we can substitute it back into the original equations to find the number of CDs each person had:
Abby: x - 23 = 71 - 23 = 48 CDs
Hakeem: x - 7 = 71 - 7 = 64 CDs
Finally, to find the total number of CDs they had together, just add up Abby's, Hakeem's, and the number of CDs Abby gave away:
Total = Abby's CDs + Hakeem's CDs + CDs Abby gave away
= 48 + 64 + 23
= 135
So, Abby and Hakeem had a total of 135 CDs together.