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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

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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