The city of Cortisville has two gas stations, Petrocort and Cortoline

BTGModeratorVI wrote: ↑

Fri Jun 05, 2020 11:47 am

The city of Cortisville has two gas stations, Petrocort and Cortoline. On a particular day, gasoline at Petrocort was sold for $2.78 per gallon and gasoline at Cortoline was sold for $3.28. If the average price per gallon for gasoline for the entire city that day was $2.99, what percent of all gasoline sold was sold at Cortoline?

A. 42%
B. 43%
C. 44%
D. 46%
E. 47%

Answer: A
Source: Veritas Prep

Weighted average of groups combined = (group A proportion)(group A average) + (group B proportion)(group B average) + (group C proportion)(group C average) + ...

Let x = the percentage of gas sold at Cortoline
This means that 100-x = the percentage of gas sold at Petrocort

As far as PROPORTIONS go, x/100 is the proportion of gas sold at Cortoline
And (100-x)/100 is the proportion of gas sold at Petrocort

Now plug the values into the weighted averages formula.
We get: 2.99 = (x/100)(3.28) + [(100-x)/100][2.78]
Eliminate the fractions by multiplying both sides by 100 to get: 299 = (x)(3.28) + (100-x)[2.78]
Expand to get: 299 = 3.28x + 278 - 2.78x
Simplify: 299 = 0.5x + 278
Subtract 278 from both sides: 21 = 0.5x
Solve: x = 42

Answer: A

BTGModeratorVI wrote: ↑

Fri Jun 05, 2020 11:47 am

The city of Cortisville has two gas stations, Petrocort and Cortoline. On a particular day, gasoline at Petrocort was sold for $2.78 per gallon and gasoline at Cortoline was sold for $3.28. If the average price per gallon for gasoline for the entire city that day was $2.99, what percent of all gasoline sold was sold at Cortoline?

A. 42%
B. 43%
C. 44%
D. 46%
E. 47%

Answer: A
Source: Veritas Prep

We can let the number of gallons sold at Petrocort = x and the number of gallons sold at Cortoline = y. Thus, the total amount of gas sold that day can be expressed as (x + y).

On a particular day, gasoline at Petrocort was sold for $2.78 per gallon and gasoline at Cortoline was sold for $3.28, and the average price per gallon for gasoline for the entire city that day was $2.99. Thus:

2.78x + 3.28y = 2.99(x + y)

278x + 328y = 299x + 299y

29y = 21x

29y/21 = x

We need to determine what percentage of all gasoline sold was sold at Cortoline, which can be expressed as y/(y+x).

Since x = 29y/21, we can substitute 29y/21 for x in the expression y/(y+x) and we have:

y/(y + 29y/21)

y/(21y/21 + 29y/21)

y/(50y/21)

21y/50y = 21/50 = 42/100 = 42%

Answer: A