Linear systems, Equations and inequalities

Question

Arthur has sold candy bars in two different sizes, small and large. He has sold 120 bars in total and made $186.00in total. If small candy bars cost $1.25 and large cost $1.75, how many of each type did he sell?

Answer 1

Here's what we know:

s + b = 120 (the small and big bars come to 120 sold)

1.25s + 1.75b = 186 (the money made from the bars is $186)

 

We can solve this by elimination by multiplying the first equation by -1.25 or -1.75, or we can go substitution by isolating one of the variables in the first equation. Let's use substitution in this case:

s = 120 - b

 

1.25(120 - b) + 1.75b = 186

150 - 1.25b + 1.75b = 186

150 + .5b = 186

.5b = 36

b = 72

 

Now to find s:

s = 120 - 72

s = 48

 

Check:

1.25 * 48 + 1.75 * 72 = 186

60 + 126 = 186

186 = 186