
Profit
Hi,
Of the $\displaystyle k$ dollars a business earns each day, $\displaystyle \frac57 k$ dollars are used to pay business expenses and the rest is profit. In terms of $\displaystyle k$, how many days will it take that business to earn a profit of $\displaystyle $1400$?
A. $\displaystyle \displaystyle \frac{200}{k}$
B. $\displaystyle \displaystyle \frac{1960}{k}$
C. $\displaystyle \displaystyle \frac{4900}{k}$
D. $\displaystyle \displaystyle 200k$
E. $\displaystyle \displaystyle 4900k$
$\displaystyle \displaystyle \frac77  \frac57 = \frac27$
$\displaystyle \displaystyle \frac27 k = 1400$
$\displaystyle \displaystyle k = 4900$
What if I divided by k: 1 = 4900/k?
Answer not available.

That is a solution choice.

hai,
first find remaining dollars per day as profit.
then
we know that product of profit/day and no. of day gives you the total profit(ie, 1400)
then u can go by options.

This looks like it is either a Level 4 or Level 5 SAT problem. That means it will be very hard algebraically, and you should only attempt an algebraic solution if you are extremely strong in algebra. I would get the answer to this by "picking numbers." I will do the problem first, then give you some remarks at the end. These remarks are very important to ensure that you transfer this knowledge to other SAT questions correctly, so make sure you read them.
I'm going to let k=7. Now I reinterpret the question.
The business earns 7 dollars each day.
5 dollars each day go to expenses.
The remaining 2 dollars each day go to profit.
How many days will it take the business to earn a profit of 1400 dollars?
I think it's quite easy to see that the answer is 700 days. Put a nice big, dark circle around this number in your test booklet. This is the answer you're looking for.
Now I plug k=7 into all five answer choices using my calculator:
(A) ~28.6 (I'm using the symbol ~ to mean approximately)
(B) 280
(C) 700
(D) 1400
(E) 34,300
Since (C) is the only answer choice that came out to 700, the answer is choice (C).
Important Remarks:
(1) I picked k=7 because I know I am going to have to divide by 7 at some point (just by glancing at the problem). This choice avoids messy fractions or decimals. k=14 would have been a good choice as well.
(2) I got the number 5 by multiplying 5/7 times 7.
(3) It is extremely important that I substituted k=7 into all five answer choices. When answering an SAT question this way it is possible for more than one answer choice to come out to the correct answer. If this happens you need to choose another value for k (but you only need to check the choices that haven't been eliminated yet).
(4) This method is more time consuming than other methods, but it makes a problem that is difficult to understand very easy to understand and solve. This should be your "fallback" method for any question that has variables in the answer choices.
(5) Just in case you don't see it, I got 700 by dividing 1400 by 2 (total profit divided by profit per day = total number of days).
Less Important Remarks:
(1) This method is not actually solving the problem. It is only eliminating answer choices. We only get the correct answer because we know that the testmakers have put a correct answer in the answer choices.
(2) In the future when you post SAT questions, I would suggest putting the question number in as well. I have a few strategies that are extremely effective but depend on knowing the difficulty level of the question.
And now for the algebraic solution: After going through the ritual of "picking numbers" you might finally be prepared to understand a quick algebraic solution.
The answer is $\displaystyle 1400\div \frac{2k}{7} = 1400\cdot \frac{7}{2k}=\frac{4900}{k}$
It is worth understanding this algebraic method, and trying to simulate it in other SAT problems to increase your level of mathematical maturity. However, I strongly recommend that you do not use this method on a hard SAT question during the actual test. It is just way too easy to get confused by the wording of the question and mess up even when you think you've done it right.