"John and Mary have some marbles. The total number of marbles with John and Mary is 75 times the ratio of the number of marbles with John to that with Mary. If Mary has 30 marbles, find the number of marbles with John. "(A) 20 (B) 30 (C) 45 (D) 50"

Question

"John  and  Mary  have  some  marbles.  The  total  number  of  marbles  with  John  and  Mary  is 75 times the ratio of the number of marbles with John to that with Mary.  If Mary has 30 marbles, find the number of marbles with John.                         "(A)  20 (B)     30 (C)     45 (D)     50"

Bytelearn · Accepted Answer

Define Variables: Let's denote the number of marbles with John as J and the number of marbles with Mary as M. According to the problem, M is given as 30. The total number of marbles is 75 times the ratio of the number of marbles with John to that with Mary. This can be written as: Total number of marbles = J + M = 75 * (J/M)Substitute Value: We know that M = 30, so we can substitute this value into the equation: J + 30 = 75 * (J/30)Multiply Equation: To solve for J, we need to get rid of the fraction. We can do this by multiplying both sides of the equation by 30: 30 * (J + 30) = 30 * 75 * (J/30)Simplify Equation: Simplifying both sides of the equation, we get: 30J + 900 = 75JIsolate Variable: Now, we need to isolate J on one side of the equation. We can do this by subtracting 30J from both sides: 30J + 900 - 30J = 75J - 30JDivide to Solve: This simplifies to: 900 = 45JTo find J, we divide both sides of the equation by 45: 900 / 45 = 45J / 45Solving for J, we get: J = 900 / 45 J = 20

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