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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?

5-kg boxes | 3-kg boxes | weight difference | |||
---|---|---|---|---|---|

guess | nos | weight | nos | weight | 5-kg boxes − 3-kg boxes |

1 | 150 | 750 kg | 150 | 450 kg | 300 kg |

2 | 170 | 850 kg | 130 | 390 kg | 460 kg |

3 | 160 | 800 kg | 140 | 420 kg | 380 kg |

Weight of 5-kg boxes = 160 × 5 kg = 800 kg.

weight of 3-kg boxes = 140 × 3 kg = 420 kg.

Total weight of the 300 boxes is 1220 kg.

Many pupils prefer the "guess and check" method as usually, less learning (and thinking) is required. However, their skill in making intelligent guesses determines the number of guesses needed to arrive at the answer. Pupils should therefore learn to analyse the results of earlier guesses to make an intelligent estimate for the next guess.

After the second guess in the above example, we can see that the required weight difference of 380 kg is midway between 300 and 460 kg. The third guess for the number of 5-kg boxes should therefore also be midway between 150 and 170 boxes.

It is in fact possible to arrive at the answer after the first guess. After the first guess, we know that another 80 kg is needed to reach the targeted weight difference of 380 kg. We also know that adding one 5-kg box (and removing one 3-kg box) increases the weight difference by 8 kg. Therefore for the second guess, we could have increased the 5-kg boxes by 80 ÷ 8 or 10 to 160 boxes.

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?

Assuming that all 300 boxes are 5-kg boxes,

weight difference = (300 × 5 kg) − (0 × 3 kg) = 1500 kg

Changing a 5-kg box to a 3-kg box

reduces the weight difference by 8 kg.

Therefore to get the targeted difference of 380 kg,

number of 5-kg boxes to change = (1500 - 380) ÷ 8 = 140 boxes

Weight of 5 kg boxes = 160 × 5 kg = 800 kg.

Number of 3 kg boxes = 140 × 3 kg = 420 kg.

Total weight of the 300 boxes is 1220 kg.

We start by assuming that all 300 boxes are 5-kg boxes. The weight difference between 300 5-kg boxes and 0 3-kg boxes is 1500 kg. The question can now be restated as "how many 5-kg boxes do we need to change (to 3-kg boxes) to get the required difference of 380 kg?".

Note: be careful if you start off with the assumption that all 300 boxes are 3-kg boxes and that the weight difference between the 3-kg and 5-kg boxes is 900 kg.

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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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