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