Answer:
Milo is 15 years old when Beth is 14 years old
Step-by-step explanation:
Let B represent the age of Beth
Let M represent the age of Milo
Given
Beth is four years older than two thirds the age of Milo is represented as:
[tex]B = 4 + \frac{2}{3} M[/tex]
Required
How old is Milo if Beth is 14 years old.
Having derived the expression for Beth and Milo's age, the next thing to do us to substitute the given parameters.
In other words
Given [tex]B = 4 + \frac{2}{3} M[/tex]
What is M if B = 14.
Substitute 14 for B
So, we have
[tex]B = 4 + \frac{2}{3} M[/tex] becomes
[tex]14 = 4 + \frac{2}{3} M[/tex]
Collect like terms
[tex]14 - 4 = \frac{2}{3} M[/tex]
[tex]10 = \frac{2}{3} M[/tex]
Multiply both sides by [tex]\frac{3}{2}[/tex]
So, we have
[tex]10 * \frac{3}{2} = \frac{2}{3} M * \frac{3}{2}[/tex]
[tex]10 * \frac{3}{2} = M[/tex]
[tex]\frac{30}{2} = M[/tex]
[tex]M = 15[/tex]
Hence, Milo is 15 years old when Beth is 14 years old
