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# If the cost of 12 eggs varies between $0.90 and$1.20, and the cost of

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Joined: 02 Sep 2009
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If the cost of 12 eggs varies between $0.90 and$1.20, and the cost of  [#permalink]

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05 Jul 2017, 04:59
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If the cost of 12 eggs varies between $0.90 and$1.20, and the cost of 5 sandwiches varies between $10 and$15, then the cost of 4 eggs and 3 sandwiches varies between

(A) $2.15 and$3.20
(B) $2.30 and$3.40
(C) $6.40 and$9.30
(D) $6.30 and$9.40
(E) $9.30 and$12.40

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If the cost of 12 eggs varies between $0.90 and$1.20, and the cost of  [#permalink]

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05 Jul 2017, 05:08
1
Since the cost of 12 eggs varies from 0.9 to 1.2$, cost of 4 eggs will vary from 0.3 to 0.4$
Similarly since cost of 5 sandwiches varies from 10 to 15$, the cost of 3 sandwiches is between 6$ and 9$This is because the cost of a single sandwich is between 2 and 3$.

Hence the cost of 3 sandwiches and 4 eggs will cost between $6.30 and$9.40(Option D)
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Re: If the cost of 12 eggs varies between $0.90 and$1.20, and the cost of  [#permalink]

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05 Jul 2017, 06:39
Bunuel wrote:
If the cost of 12 eggs varies between $0.90 and$1.20, and the cost of 5 sandwiches varies between $10 and$15, then the cost of 4 eggs and 3 sandwiches varies between

(A) $2.15 and$3.20
(B) $2.30 and$3.40
(C) $6.40 and$9.30
(D) $6.30 and$9.40
(E) $9.30 and$12.40

0.90 < 12 eggs < 1.20
Divide by 3
0.30 < 4 eggs < 0.40.................... i

Similarly,
10 < 5 sandwich < 15
Multiply by 3/5
6 < 3 sandwich < 9 ...................... ii

From i and ii , 6.30 < 4 eggs + 3 sandwiches < 9.40

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Re: If the cost of 12 eggs varies between $0.90 and$1.20, and the cost of  [#permalink]

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05 Jul 2017, 08:10
Cost of 1 egg ranges from = $$\frac{0.9}{12}$$ to $$\frac{1.2}{12}$$ = $$\frac{3}{40}$$ to $$\frac{4}{40}$$

Cost of 1 sandwich ranges from = $$\frac{10}{5}$$ to $$\frac{15}{5}$$ = $$2$$ to $$3$$

So, cost of 4 eggs and 3 sandwiches ranges from $$(4*\frac{3}{40}) + (3*2)$$ to $$(4*\frac{4}{40}) + (3*3) = (\frac{3}{10} + 6)$$ to $$(\frac{2}{5} + 9) = 6.3$$ to $$9.4$$.
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Re: If the cost of 12 eggs varies between $0.90 and$1.20, and the cost of  [#permalink]

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05 Jul 2017, 08:21
Bunuel wrote:
If the cost of 12 eggs varies between $0.90 and$1.20, and the cost of 5 sandwiches varies between $10 and$15, then the cost of 4 eggs and 3 sandwiches varies between

(A) $2.15 and$3.20
(B) $2.30 and$3.40
(C) $6.40 and$9.30
(D) $6.30 and$9.40
(E) $9.30 and$12.40

Given :
Quote:
cost of 12 eggs varies between $0.90 and$1.20

So, The max value of an egg is 0.10 & the minimum value of an egg is 0.075

Given :
Quote:
cost of 5 sandwiches varies between $10 and$15

So, The max value of a sandwich is 2 & the minimum value of an egg is 3

Quote:
then the cost of 4 eggs and 3 sandwiches varies between

Max cost of 4 eggs is 0.40 & Max cost of 3 sandwich is 6 , Total cost is 9.00
Min cost of 4 eggs is 0.30 & Min cost of 3 sandwich is 9 , Total cost is 9.30

So, the range of values is between $6.30 and$9.40, answer will be (D)
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Re: If the cost of 12 eggs varies between $0.90 and$1.20, and the cost of  [#permalink]

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06 Jul 2017, 01:09
Bunuel wrote:
If the cost of 12 eggs varies between $0.90 and$1.20, and the cost of 5 sandwiches varies between $10 and$15, then the cost of 4 eggs and 3 sandwiches varies between

(A) $2.15 and$3.20
(B) $2.30 and$3.40
(C) $6.40 and$9.30
(D) $6.30 and$9.40
(E) $9.30 and$12.40

cost of 12 eggs is ranging from 0.90 to 1.20.
divide the whole thing by 3 gives cost of 4 eggs to range from 0.30 to 0.40....(1)

cost of 5 sandwiches range from 10 to 15
divide the whole thing by 5 gives cost of 1 sandwich range from 2 to 3
cost of 3 sandwich range from 6 to 9......(2)

adding 1 and 2 gives the range 6.3 to 9.4 as the range
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Re: If the cost of 12 eggs varies between $0.90 and$1.20, and the cost of  [#permalink]

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14 Jul 2017, 10:39
Bunuel wrote:
If the cost of 12 eggs varies between $0.90 and$1.20, and the cost of 5 sandwiches varies between $10 and$15, then the cost of 4 eggs and 3 sandwiches varies between

(A) $2.15 and$3.20
(B) $2.30 and$3.40
(C) $6.40 and$9.30
(D) $6.30 and$9.40
(E) $9.30 and$12.40

We can create the following compound inequalities:

0.9 < 12e < 1.2

Since we want to know the range of 4 eggs, we can divide the inequality by 3 and we have:

0.3 < 4e < 0.4

Next we have:

10 < 5s < 15

Dividing the entire inequality by 5, we have:

2 < s < 3

Multiply the entire inequality by 3, we have:

6 < 3s < 9

Adding the two inequalities together, we have:

6.30 < 4e + 5s < 9.40

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Re: If the cost of 12 eggs varies between $0.90 and$1.20, and the cost of  [#permalink]

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29 Sep 2018, 07:41
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Re: If the cost of 12 eggs varies between $0.90 and$1.20, and the cost of   [#permalink] 29 Sep 2018, 07:41
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