SAT Math XVI

The number of green and red tomatoes can be represented by $4n$ and $3n$ , respectively, for some integer (positive and negative whole number and zero) $n$ .In this way, we can be sure that the green-to-red ratio is $4n/3n=4/3$ . We need to solve the equation:

$\frac{4n-5}{3n-5}=\frac{3}{2}$ .

Cross multiplying, $8n-10=9n-15$ so that $n=5$ . There were $3n$ , or $\boxed{15}$ , red tomatoes in the bag.

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Alternatively,

Working with the answers may be easier. If answer A is correct, then there were 16 green tomatoes and 12 red tomatoes, in order to have the 4 to 3 ratio. But removing five of each gives 11 green and 7 red, which is not in the ratio of 3 to 2. If answer B is correct, then there were 20 green tomatoes and 15 red tomatoes, since $20/15=4/3$ . Removing five of each gives 15 green and 10 red, and $15/10=3/2$ , so answer B is correct.

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Solution credit: erikthered.com

Remember that ratios must be in the most reduced form. When 5 is removed from both portions and the new ratio is not a super weird ratio like 61:80 , we can guess that the original portions were multiples of 5 .

So, 4:3 can be 20:15 or 40:30 or 80:60...etc. Let's try 20:15 , ok?

OK, take out five from each, leaving 15:10

Reduce that to get 3:2 ding ding ding

Wait, what if we chose 40:30 ? Same answer. That would go to 35:25 which is 3:2 !!!