Expensive Jacket

[heffsz]

Please take a look at the data sufficiency question below. I know that B is the answer, but don't understand the explanation that accompanied it which states that the combined payrate, (x+y), times the time, (9/20), will allow us to determine the answer. I understood 9/20 to be the combined working rate and not the time. Please advise when you have the time! Thanks

If Jim earns x dollars per hour, it will take him 4 hours to earn exactly enough money to purchase a particular jacket. If Tom earns y dollars per hour, it will take him exactly 5 hours to earn enough money to purchase the same jacket. How much does the jacket cost?

(1) Tom makes 20% less per hour than Jim does.

(2) x + y = $43.75

[Saurav]

Cost of Jacket = 4 X dollars (takes Jim 4 hours @ X dollars per hour)
Also, cost of Jacket = 5 Y (takes Tom 5 hours @ Y dollars per hour)

Hence Cost of Jacket = 4X = 5Y

In order to find the cost of the Jacket, we should be able to find either X or Y.

Consider Statement 1
Y = 0.8 X
5Y = 4X (which is same as the condition from the Question). Not Sufficient

Consider Statement 2
X + Y = 43.75

4X + 4Y = 4 * 43.75
5Y + 4Y = 4 * 43.75

hence we can find Y and hence the cost of the Jacket. Hence Statement 2 alone is sufficient.

[esledge]

Saurav is right. Just to look at (2) a different way...

From the question stem we have:
C = 4x
C = 5y
(C = cost of the jacket)

From (2) we have:
x+y=43.75

That's 3 equations with 3 unknowns (C, x, and y). Since the 3 equations are independent, we'll be able to solve for all 3 variables. The main take-away of this problem is to write every equation down, and make sure you use the equations from the question stem with each statement!

4x = 5y = 5(43.75-x)

4x = 5(43.75) - 5x
9x = 5(43.75)

Thus, x = some number, which can be plugged back in to get C = some number.