Question

A bouquet of lilies and tulips has 12 flowers. lilies cost $3 each and tulips cost $2 each the bouquet cost $32. write and solve a system of linear equations to find the number of lilies and tulips in the bouquet.

Answer 1

Let x represents the number of lilies and y represents the number of tulips in the bouquet.

As per the statement:

A bouquet of lilies and tulips has 12 flowers.

⇒x+y = 12 .....[1]

It is also given that lilies cost $3 each and tulips cost $2 each the bouquet cost $32.

⇒
`3x+2y = 32` .....[2]

Multiply equation [1] by 3 we get;

3x+ 3y = 36 .....[3]

Subtract equation [2] from [3] we get;

`3x+3y-(3x+2y)=36-32`

`3x+3y-3x-2y=36-32`

Combine like terms;

`y=4`

Substitute the value of y in [1] we get;

x + 4 = 12

Subtract 4 from both sides we get;

x = 8

Therefore, the number of lilies are 8 and the number of tulips are 4