Question

John is 5 years older than Mary. In 10 years, twice John's age decreased by Mary's age is 35, and John's age will be twice Mary's current age. Find their ages now. If x is Mary's age now and y is John's age now, which system of equations could not be used to solve the problem?

Answer 1

To solve the problem, set up a system of equations using the given information to find the ages of Mary and John. From the statement "John's age will be twice Mary's current age", we have the equation y + 10 = 2x.

Step-by-step explanation:

To solve the problem, we can set up a system of equations using the given information:

Let x be Mary's age now and y be John's age now.

From the statement "John is 5 years older than Mary", we have the equation y = x + 5.

From the statement "In 10 years, twice John's age decreased by Mary's age is 35", we have the equation 2(y + 10) - (x + 10) = 35.

From the statement "John's age will be twice Mary's current age", we have the equation y + 10 = 2x.

We can solve this system of equations to find the ages of Mary and John.

The student's question deals with two distinct concepts: algebraic systems of equations to resolve an age puzzle, and the Twin Paradox illustrating time dilation in Special Relativity. The correct algebraic system can determine John and Mary's current ages. The physics concept explains why an astronaut traveling at high speeds would age less than her twin remaining on Earth.