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ernesto baked 3 cakes in 2.5 hours. assume that the number of cakes baked varies directly with the number of hours. write and solve a direct variation equation to find how many cakes can he bake in 7.5 hours.

Verified Answer :

You would set up the equation like this: \(3=k(2.5)\)  where k is the constant of proportionality. Solve for k. k= 1.2. Now, to find how many cakes he can bake in 7.5 hours, set up the equation like this: \(c=1.2(7.5)\) . He can bake 9 cakes in 7.5 hours.

JeanaShupp

Answer: He can bake 9 cakes in 7.5 hours.

Step-by-step explanation:

Given : Ernesto baked 3 cakes in 2.5 hours.

Ratio of number of cakes time =\(\dfrac{3}{2.5}\)  (1)

Let x be the number of cakes made in  7.5 hours.

Then, Ratio of number of cakes time =\(\dfrac{x}{7.5}\)  (2)

We assume that the number of cakes baked varies directly with the number of hours.

Then from (1) and (2), we have

\(\dfrac{x}{7.5}=\dfrac{3}{2.5}\)

Multiply 7.5 on both the sides, we get

\(x=\dfrac{3}{2.5}\times7.5=9\)

Hence, he can bake 9 cakes in 7.5 hours.

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