Carlos spent $196 on 14 rose bushes and 14 geraniums.Molly spent$44 on 1 rose bush and 4 geraniums. What is the coast of one rose bush and the coast of one geranium?

Answer 1

Let r stand for the cost of rose bushes and g for the cost of geraniums.

Carlos's Equation is 14r+14g=196

Molly's Equations is 1r+4g= 44

Solve this as a systems of equation problem through eliminating either r's or g's. I'm choosing the r's to eliminate so I can solve for g. I take the second equation and multiply the whole thing by -14

14r+14g = 196

-14r+(-56g) = -616 Add both equations together

-42g= -420 divide both sides by -42..... g=$10

Take g=10 and plug it back into the original 2nd equation to find the cost of the roses.

r+4(10)=44....r+40=44....subtract both sides by 40.....r=$4

Answer 2

This type of question is best answered by using a system of equations. There are different methods for solving a system of equation. The methods which would work here are elimination or substitution.

For both methods, we need to create equations to answer the problem.

The first step in creating the equation is to define your variables. I prefer to keep variables related to what we are discussing, so I will use initials for the plants.

Rose bushes = R

Geraniums = G

Each person bought the same items but in different quantities.

Carlos: 14R + 14G = $196

Molly: 1R + 4G = $44

I will demonstrate the substitution method:

14R + 14G =196

R + 4G = 44

(I need to have one equation where I can implement it into the other equation. Because I do not have to reduce the roses, I will use that as my substitution variable.)

R + 4G = 44 (isolate the R variable)

R + 4G -4G = 44 - 4G (keep the equation balanced by doing the same operation to both sides of the equation)

R= 44 - 4G

Now put that equation to replace the variable in the other equation.

14 (44-4G) + 14G = 196

616 -56G + 14G = 196 (Combine like terms)

616-42G = 196 (Subtract 616 from both sides to have the numbers on one side and the variables on the other)

-42G = -420 (Divide by -42 on both sides)

G= 10

The price per geranium is $10

Use this number to replace the variable in the smaller equation in order to find the price of the rose bush.

44-4G = R

44 - 4(10) = R

44-40 = R

R = 4

The cost of one rose bush is $4 and the cost of one geranium is $10 according to the problem as presented above.

Answer 3

if R = Rose & G = Geranium, the

14R + 14G = 196

1R + 4G = 44

Then G = $10 & R = $4