Find the ages of John and Mary if four times John's age equals three times Mary's age, and Mary is ten years older than John.
M = J + 10
4J = 3M
Substitute J+10 for M in second equation and solve for J. Insert that value into the first equation and solve for M. Check by inserting both values into the second equation.
J= 120
M= 130
To find the ages of John and Mary, we'll start by setting up equations based on the given information.
Let's say John's age is x years.
According to the information given, Mary is ten years older than John. So Mary's age would be x + 10 years.
We are also told that four times John's age equals three times Mary's age. In equation form, this can be written as:
4x = 3(x + 10)
Now, we can solve this equation to find the value of x, which represents John's age.
Expanding the equation:
4x = 3x + 30
Combining like terms:
4x - 3x = 30
x = 30
Therefore, John is 30 years old.
To find Mary's age, we can substitute the value of x (30) into the expression x + 10:
Mary's age = 30 + 10 = 40
Therefore, John is 30 years old, and Mary is 40 years old.