SOLUTION: Justin sells brownies for$2 each and cupcakes for $3 each. Justin sells a total of 100 brownies and cupcakes for $240. Write and solve a system of linear equations to find the numb

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: Justin sells brownies for$2 each and cupcakes for $3 each. Justin sells a total of 100 brownies and cupcakes for $240. Write and solve a system of linear equations to find the numb      Log On


   

Question 1066068: Justin sells brownies for$2 each and cupcakes for $3 each. Justin sells a total of 100 brownies and cupcakes for $240. Write and solve a system of linear equations to find the number of brownies and the number of cupcakes Justin sold.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Let's set up the variables:
b = number of brownies sold
c = number of cupcakes sold

Justin sold 100 items (brownies and cupcakes only) so the two variables must add to 100
b%2Bc+=+100
which we'll refer to as equation (1).

He sells brownies for $2 each. Which means that if he sells b brownies, then he collects 2*b dollars. In addition, he sells cupcakes for $3 each. Selling c cupcakes means he collects an additional 3*c dollars.

So far, the total is 2b+3c. This total must be $240 because this is the given total he collects. The second equation, labeled equation (2), is therefore
2b%2B3c=240

The system of equations is this
system%28b%2Bc+=+100%2C2b%2B3c=240%29

------------------------------------------------------------------------------------------------
Let's use that system to find the value of b and c.

Start with equation (1). Isolate b or c. Let's get b all by itself.

b%2Bc+=+100
b%2Bc-c+=+100-c
b%2B0+=+100-c
b+=+100-c Call this equation (3)

Notice how I just subtracted c from both sides.

Now move onto equation (2). Recall that equation is 2b%2B3c=240

What we'll do from here is replace 'b' with '100-c'. This works because of equation (3) above.

2b%2B3c=240
2%28b%29%2B3c=240
2%28100-c%29%2B3c=240 Notice how b is now gone after the substitution

Now solve for c

2%28100-c%29%2B3c=240
2%28100%29%2B2%28-c%29%2B3c=240
200-2c%2B3c=240
200%2B1c=240
200%2Bc=240
c%2B200=240
c%2B200-200=240-200
c%2B0=40
c=40
Which means that Justin sold 40 cupcakes

Use the value of c to find b. We can use any equation with b & c in it. The easiest to use is equation (3).
b+=+100-c
b+=+100-40 'c' is replaced with 40 (since c = 40)
b+=+60
So 60 brownies were sold