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Tabulation and looking for pattern(s)
There are 300 boxes, some weighing 3 kg and some 5 kg. The total weight of the 5-kg boxes is 380 kg more than the total weight of the 3-kg boxes. What is the total weight of all the boxes?
| 3-kg boxes | 5-kg boxes | ||||
|---|---|---|---|---|---|
| Nos (a) | weight (b) | nos (c) | weight (d) | weight difference (d − b) | Change in difference |
| 0 | 0 kg | 300 | 1500 kg | 1500 kg | - |
| 1 | 3 kg | 299 | 1495 kg | 1492 kg | 8 kg |
| 2 | 6 kg | 298 | 1490 kg | 1484 kg | 8 kg |
| 3 | 9 kg | 297 | 1485 kg | 1476 kg | 8 kg |
| 4 | 12 kg | 296 | 1480 kg | 1468 kg | 8 kg |
Increasing the 3-kg boxes by 1 reduces the weight difference by 8 kg.
Number of 3-kg boxes required to reduce the weight difference
from 1500 kg to 380 kg = (1500 − 380) ÷ 8 or 140 boxes
Weight of 3 kg boxes = 140 × 3 kg = 420 kg.
Weight of 5 kg boxes = 160 × 5 kg = 800 kg.
Total weight of the 300 boxes is 1220 kg.
Although detailed information was not given, we could still create a table to show the effect of incremental changes to the number of 3-kg boxes. We then looked for patterns, relationships or trends in the data to help us find the answer to the question.
Note: another possible pattern is that the number of 3-kg boxes for:
weight difference of 1492 kg = (1500 − 1492) ÷ 8
weight difference of 1484 kg = (1500 − 1484) ÷ 8
weight difference of 1476 kg = (1500 − 1476) ÷ 8
weight difference of ???? kg = (1500 − ????) ÷ 8
Therefore the number of 3-kg boxes required for
weight difference of 380 kg = (1500 − 380) ÷ 8
Diagrams - model drawing
There are 300 boxes, some weighing 3 kg and some 5 kg. The total weight of the 5 kg boxes is 380 kg more than the total weight of the 3 kg boxes. What is the total weight of all the boxes?
Before: (Assume that all 300 boxes are 3-kg boxes.)
When we replace 1 unit of 3-kg boxes with 5-kg boxes, the weight (in kg) of 3-kg boxes is reduced by 3 units and the weight (in kg) of 5-kg boxes is increased by 5 units.
After: Weight of 5-kg boxes is 380 kg more than 3-kg boxes
From the 3-kg bar (A), we note that '?' + 3 units = 900 kg.
We therefore add 3 units to the 5-kg bar to resolve the unknown '?'.
8 units ⇒ ('?' + 3 units) + 380 ⇒ 900 + 380 = 1280
1 unit ⇒ 1280 ÷ 8 = 160
There are 160 5-kg boxes and 140 3-kg boxes.
Weight of 3-kg boxes = 140 × 3 kg = 420 kg.
Weight of 5-kg boxes = 160 × 5 kg = 800 kg.
Total weight of the 300 boxes is 1220 kg.
For ease of explanation, I drew separate diagrams to show the various stages (before; after; and resolving '?'). These stages can be combined into a single model diagram as shown below.
(note the slight difference in how I resolved unknown values)
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page 1 of 1 1 comment
#1, 31 Jul 07 - 06:50pmbhchia
great way of looking at it.
another way of visualizing from reasoning is to start with mid-point of 150 boxes each, ie. 150 x 5 kg = 750kg and 150 x 3 kg = 450kg, which gives a delta of 300kg.but given condition is 380 kg (difference of 80kg) more of 5-kg boxes than 3-kg boxes, means more 5 kg boxes than 3-kg. since for every 3-kg box taken out we add a 5-kg, nett increase of one 5-kg and backing out one 3-kg results in a nett increase of 8kg..hence adding 10 boxes of 5-kg (10 x 8kg = 80kg) from 150 boxes, giving 160 x 5-kg and 140 x 3-kg...ie. 1220 kg in total.
160 x 5 = 800 kg
140 x 3 = 420 kg
diff = 380 kg.
cheers
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