How old is Ling? - Explain & Show Work

Question

Yuridia is 6 years older than Ling. Jessica's age is 3 times Yuridia's age. The sum of Yuridia and Ling's ages is 17 years less than Jessica's. How old is Ling?

Answer 1

Let Y = Yuridia's age

Let L = Ling's age

Let J = Jessica's age

 

Yuridia is 6 years older than Ling 

Y = 6 + L

 

Jessica's age is 3 times Yuridia's age

J = 3Y

 

Sum of Yuridia's and Ling's age is 17 years less than Jessica's

Y + L = J - 17

 

So your equations are:

Y = 6 + L  which is the same as L = Y - 6

J = 3Y

Y + L = J - 17

 

Substitute the first equation into the third

Y + (Y - 6) = J - 17

 

Substitute the second equation into this fourth equation

Y + (Y - 6) = 3Y - 17

 

Solve for Y

 

2Y - 6 = 3Y - 17

11 = Y

So Yuridia is 11 years old

 

The question asks for Ling's age

 

L = Y - 6 = 11 - 6 = 5

So Ling is 5 years old

 

To check, J = 3Y = 3 * 11 = 33

So does Y + L = J - 17?

11 + 5 = 33 - 17?

16 = 16 YES!

So this is the right answer!