The ratio of the number of mimi’s eminem cd’s to the number of rita’s eminem cd’s is 5: 8. rita has 18 more eminem cd’s than mimi. if rita gives 22cd’s to mimi, what will be the new ratio of the number of mimi’s eminem cd’s to rita’s?
i am lost

M = Mimi’s cd’s 

R = Rita’s cd’s 

The ratio of the number of Mimi’s Eminem cd’s to the number of Rita’s Eminem cd’s is 5:8 mean: 

M / R = 5 / 8 

Rita has 18 more Eminem cd’s than Mimi mean: 

R = M + 18 

Now you have system of 2 equations with 2 unknow. 

M / R = 5 / 8 and R = M + 18 

M / R = 5 / 8 Multiply both sides by R 

M = 5 R / 8 Multiply both sides by 8 

8 M = 5 R 

Your system become: 

R = M + 18 

8 M = 5 R 

Replace R = M + 18 into equation 8 M = 5 R 

8 M = 5 ( M + 18 ) 

8 M = 5 M + 5 * 18 

8 M = 5 M + 90 Subtract 5 M to both sides 

8 M - 5 M = 5 M + 90 - 5 M 

3 M = 90 Divide both sides by 3 

M = 90 / 3 

M = 30 

Mimi has 30 cd’s 

Rita has: 

R = M + 18 = 30 + 18 = 48 

R = 48 

Rita has 48 cd’s 

If Rita gives 22cd’s to Mimi she will have 48 - 22 = 26 cd 

Mimi will have 30 + 22 = 52 cd 

The new ratio of the number of Mimi’s cd’s to Rita’s cd’s will be: 

M / R = 26 / 52 = 26 / 2 * 26 = 1:2

Distributive property