Anna grows three types of apples in her orchard: Gala, Ambrosia and Granny Smith. 2/5 of her apple trees are Gala, 1/4 of the trees are Ambrosia and the remai

Question

Anna grows three types of apples in her orchard: Gala, Ambrosia and Granny
Smith. 2/5 of her apple trees are Gala, 1/4 of the trees are Ambrosia and the
remaining 350 trees are Granny Smith. How many apple trees are in her orchard?

Answer 1

We don't know the total number of trees, so we will assign that quantity the variable x. Now, let's find the LCD of 2/5 and 1/4. It is 20.

 

2/5 = 8/20

 

1/4 = 5/20

 

The number of Gala apple trees is 2/5 x = 8/20 x

 

The number of Ambrosia apple trees is 1/4 x = 5/20 x

 

The total number apple trees, which we call x, is the sum of the number of Gala, Ambrosia, and Granny Smith apple trees.

 

x = 8/20 x + 5/20 x + 350

 

x = 13/20 x + 350

 

Can you now solve this linear equation for x?

 

 

Answer 2

Hello Gagan.

 

There are 350 Granny Smith Apple trees, and if we know what fraction of the total this is, then we can calculate the total number of apple trees.

 

We know that 2/5 are Gala, 1/4 are Ambrosia, and that the rest are Granny Smith.

 

So, the fraction that are Granny Smith (GS) = 1 - (2/5 + 1/4)

GS = 1 - (8/20 + 5/20) = 1 - 13/20 = 7/20.

 

So, 7/20 of the total number (T) is 350, or

(7/20)T = 350.

T = 350*(20/7) = 1000.

 

There are 1000 apple trees in Anna's orchard (of which 400 are Gala, 250 are Ambrosia, and 350 are Granny Smith).