Shawna spent $164 on 14 dayliles and 5 pots of ivy. Aliyah spent $46 on 2 daylilies and 12 pots of ivy. Find the cost of one daylily and the cost of one pot of ivy.

Answer 1

This is an example of a systems of equations. From the information given, we need to create two equations and solve the system of equations.

Let daylilies be represented by d, and pots of ivy represented by p.

14d + 5p = 164

2d + 12p = 46

So, let's solve the second equation for d so that we can use substitution:

2d + 12p = 46

-12p -12p

2d = 46 - 12p

2 2 2

d = 23 - 6p

Now we can substitute into the first equation:

14d + 5p = 164

14(23 - 6p) + 5p = 164

322 - 84p + 5p = 164

322 - 79p = 164

-322 -322

-79p = -158

-79 -79

p = 2

Then, we can plug that answer back into either of the original equations to solve for p. Let's use the second equation:

2d + 12(2) = 46

2d + 24 = 46

-24 -24

2d = 22

2 2

d = 11

Therefore, pots of ivy cost $2, and daylilies cost $11.

We can verify this by plugging these numbers back into either of the original equations. Let's use the first one:

14d + 5p = 164

14(11) + 5(2) = 164

154 + 10 = 164

164 = 164