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On a z day hiking trip, 4 children consumed food costing x dollars.

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On a z day hiking trip, 4 children consumed food costing x dollars. [#permalink]

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New post 07 Sep 2017, 23:28
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On a z day hiking trip, 4 children consumed food costing x dollars. For the same food costs per child per day, what would be the total cost of food consumed by 7 children during a 5 day hiking trip in terms of x and z?


A. 4z/(35x)

B. 140z/x

C. 140x/z

D. 28x/(5z)

E. 35x/(4z)
[Reveal] Spoiler: OA

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Re: On a z day hiking trip, 4 children consumed food costing x dollars. [#permalink]

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New post 07 Sep 2017, 23:36
Bunuel wrote:
On a z day hiking trip, 4 children consumed food costing x dollars. For the same food costs per child per day, what would be the total cost of food consumed by 7 children during a 5 day hiking trip in terms of x and z?


A. 4z/(35x)

B. 140z/x

C. 140x/z

D. 28x/(5z)

E. 35x/(4z)


4 C + Z D = X $
7 C + 5 D = ?? $

1 C + Z D = X/4 $
1 C + 1 D = X/4Z $
7 C + 1 D = 7X/4Z $
7 C + 5 D = 35X/4Z $

E
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On a z day hiking trip, 4 children consumed food costing x dollars. [#permalink]

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New post 08 Sep 2017, 10:30
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Bunuel wrote:
On a z day hiking trip, 4 children consumed food costing x dollars. For the same food costs per child per day, what would be the total cost of food consumed by 7 children during a 5 day hiking trip in terms of x and z?

A. 4z/(35x)

B. 140z/x

C. 140x/z

D. 28x/(5z)

E. 35x/(4z)

Divide total cost by number of children and by # of days, because we need cost of food per child per day from the first scenario to set up the equation for the second scenario.

First scenario:

\(\frac{Total Cost}{#ofDays}\) = how many dollars are available for each day, then

\(\frac{Amt.One Day}{# children}\) = amt. for 1 child for 1 day

Combine them:

Total dollars_______
(# days) * (# children)

x = total dollars for
z = # of days and
4 = # of children

Cost per child per day =

Total dollars (x)____
(z days) * (4 children)

\(\frac{x}{4z}\) = cost per child per day

Second scenario: Total cost (just reverse operations from first scenario) =

(cost per child per day) * (# of days) * (# of children)

So for 5 days and 7 children

\(\frac{x}{4z}\) * 5 * 7 =

\(\frac{35x}{4z}\)

ANSWER E

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Re: On a z day hiking trip, 4 children consumed food costing x dollars. [#permalink]

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New post 10 Sep 2017, 20:46
Bunuel wrote:
On a z day hiking trip, 4 children consumed food costing x dollars. For the same food costs per child per day, what would be the total cost of food consumed by 7 children during a 5 day hiking trip in terms of x and z?


A. 4z/(35x)

B. 140z/x

C. 140x/z

D. 28x/(5z)

E. 35x/(4z)


For z days , total cost for 4 children =x;
For 1 day per child , cost = x/4z;

For 7 children ,cost of food for 5 days = 5*7* x/4z= 35x/4z;

Ans:E

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Re: On a z day hiking trip, 4 children consumed food costing x dollars. [#permalink]

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New post 14 Sep 2017, 10:41
Bunuel wrote:
On a z day hiking trip, 4 children consumed food costing x dollars. For the same food costs per child per day, what would be the total cost of food consumed by 7 children during a 5 day hiking trip in terms of x and z?


A. 4z/(35x)

B. 140z/x

C. 140x/z

D. 28x/(5z)

E. 35x/(4z)


For the z-day hiking trip, the cost of food per child per day is (x/4)/z = x/(4z). Thus, the total cost of food for 7 children during a 5-day trip is x/(4z) * 7 * 5 = 35x/(4z).

Answer: E
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Kudos [?]: 827 [0], given: 5

Re: On a z day hiking trip, 4 children consumed food costing x dollars.   [#permalink] 14 Sep 2017, 10:41
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