Ratios and proportions

Question

The ratio of Juan's CD's to Miguel' CD's was 7 to 3. After Juan gave CDs to Miguel, they had an equal number of CDs. How many CDs did Miguel have at first? Explain and show how to reason about a strip diagram to solve this problem.

Answer 1

7:3 7/3 = J/M

3J = 7M, J=7M/3

J-x = M+ x

7M/3 = M + 2x

7M = 3M + 6x

4M = 6x

M = 6x/4 = 3x/2

J=7M/3 = 7(3x/2)/3 = 21x/6 = 7x/2

J=7x/2, M= 3x/2

J/M = 7/3 = (7x/2)/(3x/2)

if Juan gave Miguel 2 CD's Juan originally had 7 CDs and Miguel had 3 CDs

if Juan gave Miguel 4 CDs, then Juan originally had 14 CD's and Miguel had 6 CDs

if Juan gave Miguel 6 CDs then Juan originally had 21 CDs and Miguel had 9 CDs

if 8 then 28 and 12

10 then 35 and 15

12 then 42 and 18

etc.