What is the cost of one daylily and the cost of one shrub.

Question

Eduardo and Julio each improved their yards by planting day lilies and shrubs. They bought their supplies from the same store. Eduardo spent $60 on 2 day lilies and 10 shrubs. Julio spent $68 on 2 day lilies and 12 shrubs. What is the cost of one daylily and the cost of one shrub.

A) daylily: $10, shrub: $4

B) daylily: $4, shrub: $10

C) daylily: $11, shrub: $6

D) daylily: $9, shrub: $6

Answer 1

Hey Lume,

You can solve this problem by using a system of equations. First set up 2 equations to represent what is known. x= cost of day lilies and y= cost of shrubs:

equation 1: 2x + 10y= 60 (Eduardo)

equation 2: 2x + 12y = 68 (Julio)

Now solve for one of your equations (I think it's easiest to solve for x in equation 1):

2x + 10y = 60

x + 5y = 30

x=30-5y

Now you have x as a function of y and you can plug/substitute this in to x in equation 2 and solve for y:

2(30-5y) + 12y = 68

60 - 10y +12y = 68

60 + 2y= 68

2y = 8

y= 4 (so shrubs cost 4$)

Now that you know what y is, you can plug it into either equation and solve for x (I'll do equation 1):

2x + 10y = 60

2x + 10(4) = 60

2x = 20

x= 10 (so day lilies cost 10$)

Another way to solve this problem is to use the elimination method. You can add and subtract systems of equations to eliminate a variable. For example, you could subtract the 2 equations:

equation 2: 2x + 12y = 68

equation 1: 2x + 10y= 60

--------------------------

0x + 2y = 8

Now solve for y since you eliminated x:

2y = 8

y = 4

Then you can plug this back in to either equation to find x.

For this problem, the elimination method was way easier than the substitution method, but that is not always the case. I would definitely try both methods in future problems to see what you are most comfortable with. Hope this helps!

Answer 2

HI Lume

A is the correct choice

You can use a system of equations to solve for these values

Let x = daylily

Let y = shrubs

Set up the equations 1 and 2

Equation 1 for Eduardo

2x + 10y = 60

Equation 2 for Julio

2x + 12y = 68

Viewing them together should reveal that elimination works quickly with these two

2x + 10y = 60

2x + 12y = 68

Multiply Equation 1 by negative 1 this and the x will be eliminated when the equations are combined

we have

-2x -10y = -60

2x + 12y = 68

This leaves

2y = 8

Divide both sides by 2 to solve for y

y = 4

Substitute this value back into Equation 2 to solve for x

2x + 12(4) = 68

2x + 48 = 68

Subtract 48 from both sides of the equation

2x = 20

Divide both sides by 2 to solve for x

x = 10

We

Daylily cost $10 each

Shrubs cost $4 each

You can check this in the equations

Equation 1

2x + 10y = 60

2(10) + 10(4) =60

20 + 40 = 60

Equation 2

2x + 12y = 68

2(10) + 12(4) = 68

20 + 48 = 68

I hope you find this useful.

You can also try the Substitution method with the equations