Question

Gardeners plant 42 white and pink flowers in one flower bed. In another they plant 109, they want 2 times the number of white flowers and 3 times the number of pink flowers. How many white and pink flowers will there be?

Answer 1

There will be 17 white flowers and 25 pink flowers.

Explanation:

Given:

Gardeners plant 42 white and pink flowers in one flower bed.

Let number of white flowers be 'w'.

Also Let the number of pink flowers be 'p'.

So we can say that in one flower bed number of white flowers and number of pink flowers is equal to 42.

framing in equation form we get;

`w+p=42 \ \ \ \ equation \ 1`

Also Given:

In another they plant 109, they want 2 times the number of white flowers and 3 times the number of pink flowers.

So From above quote we can say that;

In another flower bed twice the number of white flowers and thrice the number of pink flowers is equal to 109.

framing in equation form we get;

`2w+3p =109 \ \ \ \ equation \ 2`

Now Multiplying equation 1 with 2 we get;

`2(w+p) = 42* 2\\\\2w+2p =84\ \ \ \ equation \ 3`

Now Subtracting equation 3 form equation 2 we get;

`(2w+3p)-(2w+2p) =109-84\\\\2w+3p-2w-2p=25\\\\p= 25`

Now Substituting the value of 'p' in equation 1 we get;

`w+p =42\\\\w+25 =42\\\\w=42-25\\\\w =17`

Hence There will be 17 white flowers and 25 pink flowers.