sandy wrote:
x > 0
Quantity A: (590+x)/800
Quantity B: (600+x)/790
Two nice rules concerning fractions with positive numerators and denominators:
1) Making a numerator bigger makes the fraction bigger.
2) Making a denominator smaller makes the fraction bigger.
So, from rule number 1, we can see that (600+x)/800 is GREATER THAN (590+x)/800
In other words,
(600+x)/800 > (590+x)/800From rule number 2, we can see that (600+x)/790 is GREATER THAN (600+x)/800
In other words,
(600+x)/790 > (600+x)/800Combine the inequalities to get:
(600+x)/790 > (600+x)/800 > (590+x)/800So, we can be certain that
(600+x)/790 > (590+x)/800Cheers,
Brent
I got the correct answer independently but I think it was just dumb luck. Can you please help steer me in the right direction if there are flaws in my logic? I simplified both QA and QB by dividing both by 10 to get QA: (59+x)/80 and QB: (60+x)/79. Then I decided that the overall impact of x was unimportant because it would be the same on both sides so I gave x a value of 1 for both quantities. I was left to compare QA: 60/80 and QB: 61/79. I decided that QB was greater because the denominator was smaller and the differences in the numerator was too minuscule to matter.