how many more green apples do you need to get 80% green apples if you have 30 red apples and 70 green apples

Question

How do I calculate this?  I know the answer is 50, I don't know how to calculate it though.  

 

 

70/100 = 70% green apples.  I need 10% more green apples.  But if I do 10 more green apples its 80/110 = 72%. 

Answer 1

Let g = the number of green apples = 70

Let r = the number of red apples = 30

Let t = the total number of apples = g + r = 100

 

We know that g / t = 0.7

 

We are asked to solve (g+x)/(t + x) = 0.8

Plug in all the values for g and t:

 

(70+x)/(70 + 30 + x) = 0.8

(70 + x)/(100 + x) = 0.8

 

 

Multiple both sides by 100+x:

70 + x = 0.8(100+x)

70 + x = 80 + 0.8x

x = 10 + 0.8x

0.2x = 10

x = 10/0.2

x = 50

 

Therefore we need 50 more green apples.

 

 

 

Answer 2

You're on the right track.  But think about it this way.  Your current percentage is:

 

70/100 = 70%

 

Every time you add a green apple then you also add another total apple, like what you said before:

 

80/110 = (about) 72%

 

But you want 80% and you don't know the amount of green apples to add is.  So lets call those x:

 

70+x/100+x = 80%

 

Since 80% is .80,

 

70+x/100+x = .8

 

70+x = .8(100+x)

 

70+x = 80+.8x

 

x = 10+.8x

 

.2x = 10

 

x = 10/.2 = 50

Answer 3

(70 + x) / (100 + x) = 0.8

70 + x = 0.8(100 + x)

 

Can you solve for x?