Maths Problem 6

Question

Solve the following word problems by first writing (an) equations and then solving the equation

John is twice as old as Mary. Five years ago he was three times as old. What is Mary’s age now?

Answer 1

Using J to represent John and M to represent Mary

 

J=2M

J-5=3(M-5)

 

The top equation says Jay is twice as old as Mary. The bottom says Jay minus five years is three times as old as Mary minus five years.

 

2M-5=3(M-5)

 

Here we replace the J from the second equation with what we defined J was equal to in the first equation (2M)

 

2M-5=3M-15

 

Distribute the right side of the equation

 

15-5=3M-2M

 

Set like terms on one side

 

10=M

 

Solve.

 

Mary is 10 years old