Question

Ashley and losa each improved their yards by planting dayliles and shrubs. They bought their supplies from the same store. Ashley spent $45 on 7 daylilies and 2 shrubs. Lisa spent $174 on 14 daylilies and 11 shurbs. What is the cost of one daylily and the cost of one scrub?

Answer 1

Let x be cost of one daylily and y be the cost of one scrub.

Ashley spent $45 on 7 daylilies and 2 shrubs. 7 daylilies cost 7x and 2 shrubs cost 2y, in total 7x+2y that is $45. The first equation is 7x+2y=45.

Lisa spent $174 on 14 daylilies and 11 shurbs. 14 daylilies cost 14x and 11 shrubs cost 11y, in total 14x+11y that is $174. The second equation is 14x+11y=144.

Solve this system. Wit hthis aim multiply first equation by 2 and the subtract second equation from first:

2·(7x+2y)-(14x+11y) =2·45-174,

14x+4y-14x-11y=90-174,

-7y=-84,

7y=84,

y=84÷7,

y=12.

Then substitute into first equation:

7x+2·12=45,

7x+24=45,

7x=45-24,

7x=21,

x=21÷7,

x=3.

Answer: the cost of one daylily is $3 and the cost of one scrub is $12.