help solve word problem by elimination.

Question

Huong and Amanda are selling cookie dough for a school fundraiser. Customers can buy packages of

sugar cookie dough and packages of oatmeal cookie dough. Huong sold 9 packages of sugar cookie

dough and 1 package of oatmeal cookie dough for a total of $49. Amanda sold 8 packages of sugar

cookie dough and 6 packages of oatmeal cookie dough for a total of $110. What is the cost each of one

package of sugar cookie dough and one package of oatmeal cookie dough?

Answer 1

Set up a system of equations:

Let s = price of sugar cookies

Let o = price of oatmeal cookies

9s + o = $49

8s + 6o = $110

To use the elimination method, multiply the first equation by -6 and then add to the second equation. This will eliminate the o term and then you can solve for s.

-6* [9s + o = $49] → -54s - 6o = -$294

[-54s - 6o = -$294] + [8s + 6o = $110] → -46s = -$184 → s = $4

Plug s into either of the original equations to solve for o:

9s + o = $49 → o = $49 - 9s = $49 - 9($4) = $49 - $36 = $13

So s = $4 and o = $13

Answer 2

Hey Eulalie,

The first step would be to make 2 different equation representing what you already know (x= cost of sugar cookie dough, and y= cost of oatmeal cookie dough):

Equation 1: 9x + y = 49 (Huong)

Equation 2: 8x + 6y = 110 (Amanda)

to solve a system of equations with the elimination method, you need to either multiply or divide all the values in one equation so the coefficients for either x or y are the same in both equations. For example, we can multiply all the values in equation 1 by 6 like this:

6( 9x + y = 49)

54x +6y = 294 (this is our new Equation 1)

Now let's look at our the new equation 1 and compare it to equation 2

Equation 1: 54x +6y = 294

Equation 2: 8x + 6y = 110

Notice how both equation have 6y in them. We can subtract the equations like this:

Equation 1: 54x +6y = 294

Equation 2: 8x + 6y = 110

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

46x + 0y = 184

46x = 184

Now that we eliminated y, we can solve for x:

46x = 184

x = 4 so sugar cookie dough costs $4

Now that you know x=4, you can plug that in to either equation 1 or 2. Let's do the original equation 1:

9x + y = 49

9(4) + y= 49

36 +y = 49

y= 13 so the oatmeal cookie dough costs $13.

Hope this helps!

Answer 3

Hi Eulalie,

I let x = the price of the sugar cookies

I let y = price of the oatmeal cookies

my two equations were then

9 x + 1 y= 49

8 x + 6 y = 110

I set y = to 49 -9 x and substituted it into the second equation.

solving one package of sugar cookies was $ 4 and one package of oatmeal was $13 .

Hope this helps.