Question

A landscaping business bought 8 rose bushes and 15 daylilies for $193. They went back later and bought 3 more rose bushes and 12 daylilies for $117. How much does each daylily cost?

Answer 1

Each daylilies cost $7

Explanation:

Step one:

let roses be x

and daylilies be y

so

8x+15y=193--------------1

also

3x+12y=117--------------2

we can solve equations 1 and 2 by substitution

8x=193-15y

x=(193-15y)/8

put x= (193-15y)/8 in 3x+12y=117

3((193-15y)/8)+12y=117

(579-45y)/8+12y=117

579-45y=8(117-12y)

579-45y=936-96y

collect like terms

579-936=-96y+45y

-357=-51y

divide both sides by -51

y=-357/-51

y=7

Hence each daylilies cost $7

put y=7 in eqn 1

8x+15(7)=193

8x+105=193

8x=193-105

8x=88

x=88/8

x=11

rose cost $8