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# Carla has 1/4 more sweaters than cardigans, and

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Carla has 1/4 more sweaters than cardigans, and [#permalink]  22 Aug 2017, 02:10
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Question Stats:

47% (11:04) correct 52% (02:28) wrong based on 21 sessions

Carla has $$\frac{1}{4}$$ more sweaters than cardigans, and $$\frac{2}{5}$$ fewer cardigans than turtle­ necks. If she has at least one of each item, what is the minimum total number of turtlenecks plus sweaters that Carla could have?

[Reveal] Spoiler: OA
35

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Re: Carla has 1/4 more sweaters than cardigans, and [#permalink]  25 Sep 2017, 07:50
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I am a bit stuck on this one. I tried to rewrite the statements as formulas and I get that
$$S=(1+\frac{1}{4})C$$
$$C=(1-\frac{2}{5}T$$
where S are sweaters, C are cardigans and T are turtlenecks.

Then, I adjusted the expression in order to build a combined one as $$S=\frac{5}{4}C=\frac{3}{4}T$$.
And I don't know how to go on.

Any hint?
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Re: Carla has 1/4 more sweaters than cardigans, and [#permalink]  25 Sep 2017, 08:52
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Carcass wrote:
Carla has $$\frac{1}{4}$$ more sweaters than cardigans, and $$\frac{2}{5}$$ fewer cardigans than turtle­ necks. If she has at least one of each item, what is the minimum total number of turtlenecks plus sweaters that Carla could have?

Given

S = $$(\frac{1}{4} +1)*C$$

= $$(\frac{5}{4})*C$$

and C = $$(1-\frac{2}{5} )*T$$

= $$(\frac{3}{5})*T$$

or T = $$(\frac{5}{3})*C$$

Now

Let C = 12 (since it is a factor of 4 and 3. It should be the minimum value)

therefore S= $$(\frac{5}{4})*12$$

or S = 15

and T =$$(\frac{5}{3})*12$$

or T = 20

Therefore the sweater and turtle neck = 15+20 =35
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Re: Carla has 1/4 more sweaters than cardigans, and [#permalink]  26 Sep 2017, 02:00
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Expert's post
$$S = ( C + \frac{1}{4} C)$$ this is the exact way to rephrase the sentence.

$$C = ( T - \frac{2}{5} T )$$

So you do have $$\frac{5}{4} C$$ and $$\frac{5}{3} T$$

Now the LCM between 4 and 3 is 12. Then substitute and you have the minimum quantity 35

Another approach is thinking real numbers, for instance: the number you are looking for must be integers.

If you think you do have 10 of C, 25% more is 2.5 so not possible. 11 you do have 2.75 BUT 12, 25% of it is 3. So it possible 12 + 3 = 15.

This is also an easy approach to follow.

Regards
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Re: Carla has 1/4 more sweaters than cardigans, and [#permalink]  11 Apr 2018, 20:02
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Since the number of Cardigans, sweaters and turtlenecks should be integers.
Given: S = C + C/4 and C = T - 2T/5 --> S = 5C/4 and T = 5C/3

Now C/4 and 5C/3 have to be integers, we would take C as an LCM of 4 and 3 i.e 12 and work out the values of C and T
Re: Carla has 1/4 more sweaters than cardigans, and   [#permalink] 11 Apr 2018, 20:02
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