Question

Simon and Greg shared pencils in the ratio 7:5. If Simon gives away 30 pencils and Greg gets 30 more pencils, they will have the same number of pencils. How many did each of them have in the beginning?

Answer 1

s/g=7/5, s=7g/5

s=g if s-30=g+30 using s found above...

7g/5 -30=g+30

(7g-150)/5=g+30

7g-150=5g+150

2g=300

g=150, and since s=7g/5, s=210

So Simon started with 210 pencils and Greg started with 150 pencils.