$84 for 3 daylilies and 6 geraniums 240 on 12 daylilies and 12 geraniums what is the cost of 1 daylily and 1 geranium

Question

Please help  trying to help autistic daughter with math

Answer 1

Set up a system of equations:

3d + 6g = $84

12d + 12g = $240

 

You can solve by elimination or substitution. Most students find substitution easier, so we'll do that.

 

First, rearrange either of the two equation to get a single variable by itself.

3d + 6g = $84

⇒ 3d = $84 - 6g

⇒ d = ($84 - 6g) / 3 = $28 - 2g

 

Then substitute into the other equation and solve for l:

12d + 12g = $240

⇒ 12($28 - 2g) + 12g = $240

⇒ $336 - 24g + 12g = $240

⇒ -12g = -$96

⇒ g = $8

 

Then substitute into either of the two original equations to solve for the other variable:

3d + 6g = $84

⇒ 3d + 6($8) = $84

⇒ 3d + $48 = $84

⇒ 3d = $36

⇒ d = $12

 

What is the cost of 1 daylily and 1 geranium?

1($12) + 1($8) = $20

Answer 2

Let's start with the first purchase and solve for daylilies (d):

3d + 6g= 84

3d= 84-6g

d= 28-2g

 

Now substitute that for d in the second purchase, then solve for g:

12(28-2g) + 12g=240

Notice the 12s on the left half of the equation. Using distributive property,

12 [(28-2g) + g]=240

28 - 2g + g = 240/12

28 - g= 20

-g = -8, so g=8

 

Then substitute the cost of geraniums (g) into the equation for the cost of daylilies:

d = 28 - 2(8)

d= 28 - 16

d= 12

 

So, the cost of 1 daylily and 1 geranium is equal to d + g, or 12 + 8= 20

Answer 3

3D + 6G = 84

12D +12G = 240

 

We can make this system easier by dividing through each of the equations by a common factor. In the first equation I'm going to divide everything by 3, and in the second by 12. Then I get this: 

 

D + 2G = 28

D + G = 20

 

If we solve both of these equations for D we get this: 

 

D = 28 - 2G 

and 

D = 20- G 

 

Since these are both expressions equal to D we can set them equal to each other: 

 

28 - 2G = 20 - G 

 

Collect like terms: 

 

28 -20 = -G + 2G 

8 = G 

 

Now substitute back into the original equation: 

D + G = 20 

D + 8 = 20 

D = 12 

 

Make sense? Thanks for working so hard to help your son.