Review 2 Ratio 1 Ravi had \( \frac{3}{5} \) as many marbles as Peter. Peter had 20 more marbles than Ravi. (a) How many marbles did the two boys have in all? (b) What was the ratio of the number of marbles Peter had to the total number of marbles both boys had?

To solve for the number of marbles each boy has, we can set up equations based on the information given. Let's denote the number of marbles Ravi has as \( R \) and the number of marbles Peter has as \( P \). From the problem: 1. \( R = \frac{3}{5}P \) 2. \( P = R + 20 \) Substituting \( R \) into the second equation: \[ P = \frac{3}{5}P + 20 \] To eliminate the fraction, multiply the whole equation by 5: \[ 5P = 3P + 100 \] \[ 2P = 100 \] \[ P = 50 \] Now, substitute back to find \( R \): \[ R = \frac{3}{5} \times 50 = 30 \] (a) Total marbles = \( R + P = 30 + 50 = 80 \) marbles. (b) The ratio of Peter's marbles (P) to the total number of marbles is: \[ \frac{P}{R + P} = \frac{50}{80} = \frac{5}{8} \] So, the two boys had 80 marbles in total, and the ratio of Peter's marbles to the total is \( \frac{5}{8} \). It's quite a marble showdown, isn’t it?