0.80d + 0.40r = 780
d + r = 1200
In these two equations, 'd' is defined as the number of people who paid the discount fare and 'r' represents the amount of people who paid the regular fare. We can make two equations out of this, since we know that the total amount of people that paid fares is 1200 (explaining the d + r = 1200). In total, the bus collected $780 (which explains the 0.80d + 0.40r = 780).
In order to solve for 'r', we'll have to isolate 'd' in the second equation (if we isolated 'r', we'd end up solving for the number of people that paid the discount fare!)
Subtract r from both sides:
d = 1200 - r
That wasn't so bad, right?
Because we now know d's value, we can input it into our first equation:
0.80(1200 - r) + 0.40r = 780
Simplify:
960 - 0.8r + 0.4r = 780
Simplify again:
960 - 0.4r = 780
Subtract both sides by 960:
- 0.4r = -180
Multiply both sides by -1 (in order to get these pesky -'s out of the way!)
0.4r = 180
Multiply by 10 (This step isn't necessary, but makes your brain hurt significantly less if you're dividing by hand)
4r = 1800
Divide both sides by 4:
r = 450
<u>450 people paid the regular fare</u>
Good luck! If you have any questions, don't be afraid to ask :))
-TB
