Solving a word problem using a system of linear equations of the form Ax + By = C

Question

A store is having a sale on walnuts and chocolate chips. For 2 pounds of walnuts and 3 pounds of chocolate chips, the total cost is $16. For 6 pounds of walnuts and 5 pounds of chocolate chips, the total cost is $34. 

Find the cost for each pound of walnuts and each pound of chocolate chips.

Cost of walnuts:

cost of Cookies:

Answer 1

Let x be Walnuts and y be Chocolate Chips.

The problem gives us the two equations:

2x + 3y = 16

6x + 5y = 34

We can use the first equation and solve for x.

So, 2x + 3y = 16 becomes x = 8 - 3/2y

We plug this in for x and the second equation becomes:

6(8 - 3/2y) + 5y = 34

Now that we have one variable, we can solve for y.

48 - 9y + 5y = 34

4y = 14

y = 7/2 or 3.5

Now that we have y, we can plug this into our equation for x and solve for x.

x = 8 - 1.5(3.5)

x = 8 - 5.25

x = 2.75

So, walnuts cost $2.75/lb. and chocolate chips cost $3.5/lb.

Answer 2

Let "w" be the cost per pound of walnuts

Let "c" be the cost per pound of chocolate chips

So 2w + 3c = 16

And 6w + 5c = 34

To solve these using elimination we could multiply both sides of the first equation by -3 to get:

-6w - 9c = -48 then placing the equations over the top of each other we can add them together like this:

-6w - 9c = -48

6w + 5c = 34

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

-4c = -14

c = -14/(-4) = 3.5

Using 2w + 3c = 16 we can plug in c = 3.5 to solve for w:

2w + 3(3.5) = 16

2w + 10.5 = 16

2w = 5.5

w = 5.5/2 = 2.75

So the cost of walnuts is $2.75 per pound and the cost of chocolate chips is $3.50 per pound