Question

you buy 8 ferns and 15 lilies for $193. your friend buys 3 ferns and 12 lilies for $117. Write and solve

Answer 1

Each fern costs $11 and each lilly costs $7

Explanation:

Let x be ferns and y be lilies

`8x+15y=193\\3x+12y=117`

Let's solve for 3 in the second equation.

`3x+12y=117\\3x=117-12y\\x=(117-12y)/(3)`

Now replace x in the first equation.

`8x+15y=193\\8((117-12y)/(3))+15y=193\\ (936-96y)/(3)+15y=193`

Break down the fraction.

`(936)/(3)-(96)/(3)y+15y=193`

`312-(96)/(3)y+15y=193`

Subtract 312

`-(96)/(3)y+15y=193-312`

Combine like terms;

`(-96+3*15)/(3)y=-119`

Solve;

`(-96+45)/(3)y=-119`

`(-51)/(3)y=-119`

`-17y=-119`

Divide by -17

`y=(-119)/(-17)\\ y=7`

Now replace y in any of the equations to find x.

`3x+12y=117\\3x+12(7)=117\\3x+84=117\\3x=117-84\\3x=33\\x=(33)/(3)\\ x=11`