Harvey is 3 times as old as Jane. The sum of their ages is 48 years. What is the age of each?

Question

Eva Abramson · Accepted Answer

#"Jane's' age" = 12years and "Harvey's age" = 36years#

Let #"Jane's' age" = x#

Hence, Harvey is #3 xx# as old as Jane

#:. "Harvey's age" = 3 xx x = 3x#

Sum of their ages..

#"Jane's' age" (x) + "Harvey's age" (3x) = 48#

#x + 3x = 48#

#4x = 48#

Divide both sides by #color(red)4#

#(4x)/color(red)4 = 48/color(red)4#

#cancel(4x)/cancel4 = 48/4#

#x = 48/4#

#x = 12#

Substituting each values..

#"Jane's' age" = x#

#"Jane's' age" = 12years#

and..

#"Harvey's age" = 3x#

#"Harvey's age" = 3(12)#

#"Harvey's age" = 36years#

Ethan Adkins · Answer

undefined Let's denote Jane's age as J and Harvey's age as H. Given that Harvey is 3 times as old as Jane, we can write the equation H = 3J.

Since the sum of their ages is 48 years, we can write another equation: J + H = 48.

Now, we can substitute the expression for H from the first equation into the second equation: J + 3J = 48.

Combining like terms, we get 4J = 48.

Dividing both sides by 4, we find that J = 12.

Now, we can use this value to find H: H = 3 * 12 = 36.

So, Jane is 12 years old and Harvey is 36 years old.