Joseph is four years younger than Mary, if three times Mary’s equals

four times Joseph’s age, find: a) Mary’s age b) Joseph’s age

Mary's age ---- x

Joe's age ----- x-4

3x = 4(x-4)

solve for x

To solve this problem, let's start by setting up some equations based on the given information:

Let's assume Mary's age is represented by M, and Joseph's age is represented by J.

Given that Joseph is four years younger than Mary, we can write the equation: J = M - 4 ----(1)

Given that three times Mary's age equals four times Joseph's age, we can write the equation: 3M = 4J ----(2)

Now we have a system of two equations with two variables. We can solve this system to find the values of Mary's and Joseph's ages.

Step 1: Substitute equation (1) into equation (2) to eliminate J:
3M = 4(M - 4)

Step 2: Distribute the 4 on the right side of the equation:
3M = 4M - 16

Step 3: Move all the M terms to one side and the constant term to the other side of the equation:
4M - 3M = 16

Step 4: Simplify the left side of the equation:
M = 16

This means Mary's age is 16 years old.

Step 5: Substitute M = 16 into equation (1) to find Joseph's age:
J = 16 - 4

Simplifying further:
J = 12

Therefore, Joseph's age is 12 years old.

To summarize:
a) Mary's age is 16.
b) Joseph's age is 12.

So, Mary is 16 years old and Joseph is 12 years old.