SOLUTION: In 2 years, Mr. Victoria will be thrice the age of his son Bing. Six years ago, he was 5 times Bing's age. How old is each at present? I need the solution please. :(

Hi, there--

THE PROBLEM:
In two years, Mr. Victoria will be thrice the age of his son, Bing. Six yeas ago, he was five times 
Bing's age. How old is each at present?

A SOLUTION:
This is a solution using two variables. One can also solve this using only one variable. (Please 
email be if you would like to see the one-variable solution.)

Let v be the age of Mr. Victoria at present.
Let b be the age of Bing at present.

Write two equations modeling the relationships is the problem.
FIRST EQUATION: "In two years, Mr. Victoria will be thrice the age of his son, Bing."

In two years, Mr Victoria will be 2 years older so his age will be v+2.
In two years, Bing's age will be b+2.

Mr. Victoria will be thrice (three times) the age of Bing, so our equation is
v + 2 = 3*(b + 2)

SECOND EQUATION: "Six yeas ago, he was five times Bing's age."
Six years ago, Mr. Victoria was 6 years younger; his age was v-6.
Likewise, Bing 's age was b-6.

Mr. Victoria was 5 times Bing's age, so our equation is
v-6 = 5*(b - 6)

We now have a system of two equations in two variables. We can solve for v and b using the 
substitution method.

Simplify the first equation and rewrite in"v=" form.
v + 2 = 3*(b + 2)
v + 2 = 3b + 6
v = 3b + 6 - 2
v = 3b + 4

Substitute 3b + 4 for v in the second equation.
v - 6 = 5*(b - 6)
(3b + 4) - 6 = 5*(b - 6)

Simplify and solve for b.
3b + 4 - 6 = 5b - 30
3b - 2 = 5b - 30

Subtract 5b from both sides of the equation. (3b-5b=-2b and 5b-5b=0)
-2b - 2 = -30

Add 2 to both sides of the equation. (-2+2=0)
-2b = -28

Divide both sides of the equation by -2. (-2b/-2=b and -28/-2=14)
b = 14

In the context of this problem, b=14 means that Bing is 14 years old at present. We can use 
either equation to determine Mr. Victoria's age. I'll use the first equation we simplified.

v = 3b + 4
v = 3(14) + 4
v = 42 + 4
v = 46

The equation v=46 means that Mr. Victoria is 46 years old at present.

It's a good idea to check your numbers with the wording of the original problem.
"In two years, Mr. Victoria will be thrice the age of his son, Bing."
In two years, Mr. Victoria will be 48 and Bing will be 16. We know that 46 is thrice 16. CHECK!

"Six yeas ago, he was five times Bing's age."
Six years ago Mr. Victoria was 40 and Bing was 8. We know that 40 is 5 times 8. CHECK!


Hope this helps! Feel free to email me if you has questions about this (or want the 
one-variable solution.)

Mrs. Figgy
math.in.the.vortex@gmail.com