The ratio of the number of Eminem CDs Mimi has to the number of Eminem CDs Rita has is 5:8. Rita has 18 more Eminem CDs than Mimi. If Rita gives 22 CDs to Mimi, what will be the new ratio of the number Eminem CDs Mimi has to the number of Eminem CDs Rita has?

2:1

Step-by-step explanation:

Hi, to answer this question we have to write a system of equations  

R = M+18 (Rita(R) has 18 more Eminem CDs than Mimi(M))

M/R= 5/8 (ratio)

Solving for M (Mimi's cds) in the second equation

8M=5R

M=5/8R

Replacing M =5/8R in the first equation

R=5/8R +18

R-5/8R= 18

3/8R =18

R=18 /(3/8)

R= 48 CDS

Back in the second equation

8M =5R

8M=5(48)

8M= 240

M= 240/8

M=30 CDS

If Rita gives 22 CDs to Mimi

R=48-22=26

M=30+22=52

The new ratio of the number Eminem CDs Mimi has to the number of Eminem CDs Rita has IS:

M/R= 52/26= 26x2 /26 x1 = 2/1 =2:1

Feel free to ask for more if needed or if you did not understand something.