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In-service program documentation
Exploring implications for assessment (D5.3)
Participants' solutions to item from innovative statewide test
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| Text of test item |
| Solutions: 1, 2, 3, 4, 5 |
Test item:
The local sports complex charges different prices for their tickets to different sporting events. The table below shows their current prices. [Anyone under 16 years of age would pruchase a child's ticket.]
Ticket Prices
| Child | Adult | |
| Hockey | $4.50 | $7.00 |
| Basketball | $5.00 | $9.00 |
| Football | $6.25 | $11.50 |
Ken's Scout Troop earned money in order to go to Saturday's football game. His father bought 8 tickets for the scouts and one ticket for himself as the Scoutmaster.
When Ken's father pays for the tickets, how much change will he receive from a $100 bill?
Solution 1:
The problem is not well enough defined to answer the question -- we don't know how many scouts are under 16 and how many are over 16 and therefore pay adult prices.
If we assume that most kids lose interest in scouting before Age 16 then the amount of change can be calculated assuming all scouts are under 16.
6.25x
8
50.00
11.50
61.50
$35.50 using the assumption that no scout are under 16.
*We must assume also that Ken's father is over 16 years of age and not getting complimentary tickets as scout leader.
Solution 2:
9 tickets
| 6.25 | 100.00 | |
| x 8 | 61.50 | |
| 50.00 | kids | 38.50 |
| 11.50 | adult | |
| 61.50 |
$ 38.50 change from 100.00 if all scouts are under 16.
His change will be $38.50 depending on the number of scouts that are under the age of 16.
Solution 3:
| If all are under 16: | If all 16: | ||||
| 1*11.50 + 8*6.25 | change | 9*11.50 | 8*11.50 + 1*6.25 | ||
| (61.50) | (103.5) | (98.25) | |||
| $38.50 change | $ 3.50 change |
$ 3.50 change $38.50
incremented: not really all values between $3.50 and $38.50 -- the kids need to be whole.
Solution 4:
| Adults | Children | |
| 1 | 8 | 61.50 |
| 2 | 7 | 66.75 |
| 3 | 6 | 72.25 |
| 4 | 5 | 77.25 |
| 5 | 4 | 82.50 |
| 6 | 3 | 87.75 |
| 7 | 2 | 93.00 |
| 8 | 1 | 98.25 |
| 9 | 0 | 103.50 |
$38.50 change if all under 16.
Click to see Solution 5
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