A ferry can carry a maximum of 25 adults or 35 children. A ticket for an adult cost $40 and a ticket for a child cost $20. A group of adults and children took 4 such ferries at maximum load on a ferry trip. The total amount paid for the children was $2300 less than the total amount paid for the adults.
- How many adults were there?
- How many children were there?
Number of adults |
Amount paid for adults |
Number of children |
Amount paid for children |
Difference in total amounts paid |
100 |
100 x 40 = 4000 |
0 |
0 x 20 = 0 |
4000 - 0 = 4000 |
- 5 |
|
+ 7 |
|
- 340 |
95 |
95 x 40 = 3800 |
7 |
7 x 20 = 140 |
3800 - 140 = 3660 |
75 |
|
35 |
|
2300 |
25 adults → 35 children
(÷5)5 adults → 7 children
From every decrease of 5 adults, there is an increase of 7 children and the difference in the total amounts paid between the adults and the children will be reduced by $340.
If all 4 ferries are occupied by only adults, total number of adults
= 4 x 25
= 100
Total difference
= 4000 - 2300
= $1700
Small difference
= 4000 - 3660
= $340
Number of sets
= 1700 ÷ 340
= 5
Total decrease in the number of adults
= 5 x 5
= 25
(a)
Number of adults
= 100 - 25
= 75
(b)
Number of children
= 5 x 7
= 35
Answer(s): (a) 75; (b) 35