Question

Sydney and Elijah are working on creating a garden. They go to the store and buy 29 flower stems and spent $120.94. Elijah and Sydney only bought lilies and peonies, lilies cost $3.42 per stem and peonies cost $4.78 per stem. How many lily stems did they buy? How many peony stems did they buy?

Answer 1

Given:

Total number of flower they buy = 29 stems

Total cost = $120.94

Lilies cost = $3.42 per stem

Peonies cost = $4.78 per stem

To find:

The number of lily stems and peony stems did they buy.

Solution:

Let number of lily stems = x

Number of lily stems and peony stems = y

According to given information,

`x+y=29` ...(i)

`3.42x+4.78y=120.94` ...(ii)

From (i) and (ii), we get

`3.42x+4.78(29-x)=120.94`

`3.42x+138.62-4.78x=120.94`

`-1.36x=120.94-138.62`

`-1.36x=-17.68`

Divide both sides by -1.36.

`x=(-17.68)/(-1.36)`

`x=13`

Put x=13 in (i).

`13+y=29`

`y=29-13`

`y=16`

Therefore, number of lily stems is 13 and number of lily stems and peony stems is 16.