Original Amount

[Guest]

An apple grower has 2 trees with one color apples - one only has green apples and the other only red apples. All of the apples were picked from both trees and was discovered there were 5 red apples for every 4 green apples. An amount of 16 red and 16 green were consumed. The remainder were counted and there were 3 red for every 2 green. Determine original amount of each color.

Let G = green
Let R = red

My partial solution:

5:4

G - 16
R - 16

3:2

How do I continue ?

[Guest]

R/G = 5/4 .....this means G = 4R/5

(R-16)/(G-16) = 3/2

(R-16)/(4R/5-16) = 3/2

cross multiply.....

2(R-16) = 3(4R/5-16)

2R - 32 = 12R/5 - 48

48 - 32 = (12R/5 - 2R) = (12R/5 - 10R/5)

16 = 2R/5

80 = 2R

40 = R

G = 4R/5 = 160/5 = 32

Answer .... 40 Red apples and 32 Green apples.

[Guest]

Thanks again.

A question:

"R/G = 5/4 .....this means G = 4R/5" Why is G = 4R/5 ?

[Guest]

A question:

"R/G = 5/4 .....this means G = 4R/5" Why is G = 4R/5 ?
5 green for every 4 red.......
For every Green there is a corresponding 4/5 Red

5 times 4/5 is 20 fifths, equals 4

[Guest]

"All of the apples were picked from both trees and was discovered there were 5 red apples for every 4 green apples."

"5 green for every 4 red......." Should it read 5 red for every 4 green ?

[Guest]

Yes, sorry about that.........
The ratio of Red to Green is 5 to 4..... R:G = 5:4

"R/G = 5/4 .....this means G = 4R/5" Why is G = 4R/5 ?
5 Red for every 4 Green.......
For every Green there is a corresponding 4/5 Red

5 times 4/5 is 20 fifths, equals 4

[Guest]

I understand now - thanks again.

[Guest]

A follow-up:

Just to check the answer - 40/32 = 5/4 24/16 = 3/2 ??

Thank you.