Question

A city bus collected $780 in fares on one day.

The price of a regular fare was $0.80, and the
price of a discount fare was $0.40. If a total of
1200 people paid the fares on this bus, how
many people paid the regular fare?

Answer 1

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

450 people paid the regular fare

Good luck! If you have any questions, don't be afraid to ask :))

-TB

Answer 2

450 people paid the discounted fare and 750 people paid the regular fare.

Explanation:

let r be regular fares paid and d be discounted fares paid

Total fares = 0.8r + 0.4d = 780

Since 1200 people paid the fares,

r + d = 1200 = Total people

Rearrange this formula:

r = 1200 - d

Substitute r into Total Fares formula

Total fares = 0.8r + 0.4d

780 = 0.8(1200-d) + 0.4d

780 = 960 - 0.8d + 0.4d

780 = 960 - 0.4d

0.4d = 180

d = 450

Sub d=450 into Total people formula

r + d = 1200 = Total people

r + 450 = 1200

r = 1200-450

r = 750

450 people paid the discounted fare and 750 people paid the regular fare.