Albert packed a total of 306 card games and board games into 23 boxes. The card games and board games were packed in separate boxes. Each box could hold either 18 card games or 6 board games only.
- How many board games were there in all?
- Jaslyn paid a total of $1422 for all the card games and board games. The cost of one board game is $17. Find the total cost of the card games.
Boxes of card games |
Number of card games |
Boxes of board games |
Number of board games |
Total number of games |
23
|
23 x 18 = 414 |
0
|
0
|
414
|
22
|
22 x 18 = 396 |
1
|
1 x 6 = 6 |
402 |
14
|
14 x 18 = 252 |
9
|
9 x 6 = 54 |
306
|
(a)
Total number of games if all are card games
= 18 x 23
= 414
Big difference between the number of boxes of card games and boxes of board games
= 414 - 306
= 108
Small difference between the number of 1 box of card games and 1 box of board games
= 18 - 6
= 12
Number of boxes of board games
= 108 ÷ 12
= 9
Total number of board games
= 9 x 6
= 54
(b)
Total cost of board games
= 54 x 17
= $918
Total cost of card games
= 1422 - 918
= $504
Answer(s): (a) 54; (b) $504