19. The number of of Kristen's marbles 25 more than that of 20% 1 3 was of John's marbles. They had a total of 315 marbles. Kristen gave John some marbles and the ratio of the number of marbles Kristen had left to the ratio of the number of marbles John had left became 29: 34. What was the number of marbles Kristen gave to John?
Question
- The number of of Kristen's marbles 25 more than that of 20% 1 3 was of John's marbles. They had a total of 315 marbles. Kristen gave John some marbles and the ratio of the number of marbles Kristen had left to the ratio of the number of marbles John had left became 29: 34. What was the number of marbles Kristen gave to John?
Solution
Let's break down the problem step by step:
Step 1: Let's denote the number of John's marbles as J. According to the problem, Kristen has 25 more marbles than 20% of 1/3 of John's marbles. This can be written as K = (1/3)0.2J + 25.
Step 2: We also know that the total number of marbles they have is 315. So, we can write another equation: J + K = 315.
Step 3: Now we have a system of two equations, and we can solve it to find the values of J and K.
Step 4: After Kristen gave John some marbles, the ratio of the number of marbles Kristen had left to the number of marbles John had became 29:34. Let's denote the number of marbles Kristen gave to John as x. So, we can write the equation: (K-x)/(J+x) = 29/34.
Step 5: Now we have another equation with one unknown, and we can solve it to find the value of x, which is the number of marbles Kristen gave to John.
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