abyatl72 wrote:The ratio of new cars to old cars in a certain city subway system is 5:3.
If 9 tenths of the new cars are considered "Graffiti free", which of the following is the largest possible ratio of "Graffiti free" cars to non-graffiti free cars in the entire system?
Thank you so much Aby from Mexico
Hi Aby from Mexico! It's cold up here today, I wish I were on a Mexican beach instead!
To find the greatest possible ratio of a:b, you want to maximize a and minimize b.
So, if we want the largest possible ratio of graffiti free to non-graffiti free cars, we want to maximize the # of cars without graffiti and minimize the number of cars with graffiti.
We know that 9/10 of the new cars are graffiti free, but we're not told anything about the old cars. Since we want to maximize "graffiti free", let's say that ALL of the old cars fall into this category.
Further, let's pick numbers to make this question easier. We want the number of new cars to be divisible by 10, and we have another ratio of 5:3, so let's say we have a total of 80 cars.
Accordingly:
Number of new cars = 50, number of old cars = 30
Of the new cars, .9(50) = 45 are graffiti free, 5 have graffiti
Of the old cars, all 30 are graffiti free.
So, graffiti free:graffiti = 75:5 = 15:1
