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