Mary had 552 purple and green ribbons. She gave 48 purple ribbons and 1/5 of the green ribbons.

Question

The number of green ribbons left was twice the number of purple ribbons left. How many green ribbins did Mary have at first?

Answer 1

p = purple ribbons

g = green ribbons

p+g = 552

purple ribbons left = p-48

green ribbons left = 4g/5

"The number of green ribbons left was twice the number of purple ribbons left."

4g/5 = 2(p-48)

4g/5 = 2p-96

4g = 10p-480

-10p + 4g = -480            (rearranged)

10p + 10g = 5520           (add 10 times p+g = 552)

           14g = 5040

g = 360

 

Answer 2

 

Total ribbons:

P + G = 552

 

Where;

P = number purple Mary had at first

G = number of green Mary had at first

 

She gave 48 purple (P - 48) ribbons and 1/5 of the green ribbons (G/5 given away, 4G/5 left over). The number of green ribbons left was twice the number of purple ribbons left.

 

2(P - 48) = 4G/5

 

Using the first total ribbon equation:

 

P + G = 552

P = 552 - G

 

Substitute this in for P in the second equation.

 

2(P - 48) = 4G/5

 

2(552 - G - 48) = 4G/5

 

2(504 - G) = 4G/5

 

distribute the 2

 

1008 - 2G = 4G/5

 

multiply both sides by 5

 

5040 - 10G = 4G

 

add 10G to both side

 

5040 = 4G + 10G

 

5040 = 14G

 

divide both sides by 14

 

360 = G