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M11-36

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Bunuel
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M11-36 [#permalink] New post   16 Sep 2014, 00:45
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Due to weight constraints, a lorry can transport a maximum of 20 crates of apples. The weight of a crate of oranges is \(\frac{3}{4}\) that of a crate of apples. If the lorry already has 10 crates of apples loaded, what is the maximum number of crates of oranges it can still accommodate?

A. 8
B. 9
C. 12
D. 13
E. 14
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D
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Bunuel
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Re M11-36 [#permalink] New post   16 Sep 2014, 00:45
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Official Solution:

Due to weight constraints, a lorry can transport a maximum of 20 crates of apples. The weight of a crate of oranges is \(\frac{3}{4}\) that of a crate of apples. If the lorry already has 10 crates of apples loaded, what is the maximum number of crates of oranges it can still accommodate?

A. 8
B. 9
C. 12
D. 13
E. 14


There's still space for 10 crates of apples on the lorry. Since one crate of oranges weighs \(\frac{3}{4}\) the weight of a crate of apples, this means one crate of apples weighs \(\frac{4}{3}\) of a crate of oranges. Therefore, the weight of 10 crates of apples is equivalent to the weight of \(10*(\frac{4}{3}) = 13\frac{1}{3}\) crates of oranges. As the number of crates must be a whole number, the lorry can additionally accommodate a maximum of 13 crates of oranges.


Answer: D
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KarishmaB
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Re: M11-36 [#permalink] New post   03 Oct 2022, 04:46
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ayakik wrote:
I got this right based on intuition, but I'm having a difficult time trying to set up a formula, and I'm worried that I would get this wrong if the wording was more complex. Since it's 1:3/4 apples to oranges, I saw that we could divide 10 by 3/4 to get the equivalent number of oranges. Is there any other way to explain the set up? Is it because it's 1 apple/ per 3/4 oranges = 1/(3/4) = 4/3? I would really appreciate any guidance.

Bunuel KarishmaB avigutman


We need to find the number of crates of oranges which are equivalent to 10 crates of apples (leftover weight)

Total weight of orange crates to be loaded = total weight of 10 crates of apples

No of orange crates * weight of orange crates = 10 * weight of apple crates

If the weight of an apple crate is w, the weight of an orange crate is (3/4)w.

No of orange crates * (3/4)w = 10 * w

No of orange crates = 40/3 = 13.33 so 13


Note that we do not need to go through this entire process to get the answer. Consider that the total weight of orange crates will be the same as the weight of 10 crates of apples. So if the weight of each crate of orange is (3/4)th, you can take (4/3) more orange crates i.e. you can take 10 * (4/3) = 13 orange crates.

I like to imagine this equation:

Number1 * weight1 = Number2 * weight2

If
\(Number1 * weight1 = Number2 * \frac{3}{4} * weight1\)

then
\(Number1 * weight1 = \frac{4}{3} * Number1 * \frac{3}{4} * weight1\)
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Re: M11-36 [#permalink] New post   02 Oct 2022, 13:43
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ayakik wrote:
I got this right based on intuition, but I'm having a difficult time trying to set up a formula, and I'm worried that I would get this wrong if the wording was more complex. Since it's 1:3/4 apples to oranges, I saw that we could divide 10 by 3/4 to get the equivalent number of oranges. Is there any other way to explain the set up? Is it because it's 1 apple/ per 3/4 oranges = 1/(3/4) = 4/3? I would really appreciate any guidance.

Bunuel KarishmaB avigutman

Intuition is much better than a formula, ayakik!
If we were told that the weight of a crate of oranges is double the weight of a crate of apples, most people would be able to intuitively "see" that the lorry can accommodate half as many crates of oranges.
The bold faced words in my previous sentence are reciprocals of one another. This gets a lot less intuitive for people when the ratio can't be described as "double", "triple", "six times as many", etc. But the logic is the same logic. Weight of a crate and number of crates have a reciprocal relationship in this problem.
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Re: M11-36 [#permalink] New post   28 Jul 2017, 22:30
Let's say, the weight of one crate of apples is 4 kg

So, the wt of one crate of oranges becomes 3/4(4) = 3 kg

Capacity of truck is 4kg * 20 crates =80 kg

10 crates of apples is already loaded i.e 40 kg and the balance capacity is 80-40=40 kg

No of crates of orages, the truck can accomodate is 40/3 = 13.33 = 13 crates
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Re: M11-36 [#permalink] New post   01 Oct 2022, 08:18
I got this right based on intuition, but I'm having a difficult time trying to set up a formula, and I'm worried that I would get this wrong if the wording was more complex. Since it's 1:3/4 apples to oranges, I saw that we could divide 10 by 3/4 to get the equivalent number of oranges. Is there any other way to explain the set up? Is it because it's 1 apple/ per 3/4 oranges = 1/(3/4) = 4/3? I would really appreciate any guidance.

Bunuel KarishmaB avigutman
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Bunuel
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Re: M11-36 [#permalink] New post   16 Oct 2023, 09:16
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I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.
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Re: M11-36 [#permalink]
16 Oct 2023, 09:16
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