Algebra 1 word problems

Question

Chelsea and Gabriella are selling cookie dough for a school fundraiser. Customers can buy

packages of white chocolate chip cookie dough and packages of double chocolate cookie dough.

Chelsea sold 7 packages of white chocolate chip cookie dough and 4 packages of double

chocolate cookie dough for a total of $112. Gabriella sold 14 packages of white chocolate chip

cookie dough and 2 packages of double chocolate cookie dough for a total of $140. What is the

cost each of one package of white chocolate chip cookie dough and one package of double

chocolate cookie dough?

 

Answer 1

Let's call the price of the white chocolate chip cookie dough W, and the double chocolate chip cookie dough D.

That Chelsea sold 7 packages of the white and 4 of the double for a total of 112 means

7W+4D=112

Likewise, since Gabriella sold 14 white and 2 of the double for a total of 140 menas

14E+2D=140

From here, you need to use your techniques for solving systems of equations. I prefer to multiply each equation by some number that one of the coefficients match, and then subtracting. In this case, I'll multiply Gabriella's equation by 1/2 to get

7W+4D=112 (Chelsea)

7W+1D=70 (Gabriella)

Now, I can subtract these two equations. On the left hand side, the 7Ws cancel, and I'm left with

3D=42

D=14

Now that I have D, I can go back into either equation to get W. I'll use Gabriella's equation after multiplying by 1/2

7W+1D=70 -> 7W+14=70 -> 7W=56 -> W=8

So the price of the white chocolate chip cookie dough is $8, and the double chocolate chip cookies dough is $14.

Answer 2

Hi Juliana T.

White Chocolate Chip Cookie Dough costs $8 per package

Double Chocolate Cookie Dough costs $14 per package

You can use a system of equations to solve for the prices

Let x = white chocolate chip cookie dough

Let y = double chocolate cookie dough

You have the totals and amounts for both Chelsea and Gabriella

Chelsea

7x + 4y = 112

Gabriella

14x + 2y = 140

I will use elimination to solve you can also use substitution

First I will Multiply Chelsea by -2,

-2(7x + 4y = 112) to give

-14x - 8y = -224

Next I will add it to Gabriella to eliminate x and solve for y

-14x - 8y = -224

14x + 2y = 140

The x term is eliminated because -14x + 14x = 0 leaving

-6y = -84

Divide both sides by -6 to solve for y

y = 14

Plug this y value into either original equation to solve x. I will plug it into Gabriella

14x + 2y = 140

14x + 2(14) = 140

14x + 28 = 140

Next subtract 28 from both sides of the equation

14x = 140 - 28

14x = 112

Divide both sides of the equation by 14

x = 112/14= 8

Finally checking and I will use Chelsea to check

7x + 4y = 112

7(8) + 4(14) = 112

56 + 56 =112

112 = 112

So White Chocolate Chip Cookie Dough costs $8 dollars per package and Double Chocolate Cookie Dough costs $14 per package