The ratio of red to blue counters in a bag is 1: 4.2 red counters are added, now the ratio of red to blue is 1: 2.how many counters were in the bag originally. i have the answer (which is 10) i just need an explanation

10

Step-by-step explanation:

So, there are at least 5 counters in the beginning. If we add two more, that makes 7, which does not make sense with the 1:2 ratio since it cannot be divided by 3. If we double the amount of counters, that makes it 10 in the beginning, and we add two more, which equals 12. 12 is dividable by three, making the ratio of 1:2 make sense, which each unit in the ratio being 4 counters. That means there are now 12 counters. Subtract two and you get the beginning amount.

I hope this helps!

step-by-step explanation:

∆abc has the points a(1, 7), b(-2, 2), and c(4, 2) as its vertices. formed with the point d(1, 2) as its third vertex, then ∆abd is triangle.

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step-by-step explanation: