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...
ratios are just fractions. So, you have
a = h
(a-23)/(h-7) = 3/4
now just solve for a,h and then a+h
To solve this problem, we can set up an equation based on the given information. Let's assume that both Abby and Hakeem initially had x CDs.
After Abby gave away 23 CDs, she was left with x - 23 CDs.
After Hakeem sold 7 CDs, he was left with x - 7 CDs.
The ratio of CDs became 3:4, which means the remaining CDs can be expressed as (3/4) * x for Abby and (4/4) * x for Hakeem.
Setting up the equation:
(3/4) * x = x - 23 - 7
Let's solve it step by step:
First, multiply both sides of the equation by 4 to get rid of the fraction:
3x = 4(x - 30)
Simplify the equation:
3x = 4x - 120
Next, subtract 4x from both sides to isolate the x term:
3x - 4x = -120
Simplify further:
-x = -120
Multiply both sides by -1 to solve for x:
x = 120
So, Abby and Hakeem each had 120 CDs initially.
To find the total number of CDs they all had together, we add:
Abby's CDs initially (x) + Hakeem's CDs initially (x) = 120 + 120 = 240 CDs in total.
Thus, they all had a total of 240 CDs together.