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

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) (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

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

The system of equations is this

------------------------------------------------------------------------------------------------
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.

Call this equation (3)

Notice how I just subtracted c from both sides.

Now move onto equation (2). Recall that equation is

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

Notice how b is now gone after the substitution

Now solve for c

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).

'c' is replaced with 40 (since c = 40)

So 60 brownies were sold
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