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?

7/5=s/g multiply both sides by g

7g/5=s  multiply both sides by 5/7

g=5s/7

We are then told that:

g+30=s-30  subtract 30 from both sides

g=s-60, and from earlier g=5s/7, and g=g so we can say:

s-60=5s/7  multiply both sides by 7

7s-420=5s  subtract 5s from both sides

2s-420=0  add 420 to both sides

2s=420 divide both sides by 2

s=210, and since g=s-60

g=150

So Simon had 210 pencils and Greg had 150 pencils.

Check..

s:g=210:150=7:5

and

s-30=g+30

210-30=150+30

180=180