Question

Gabrielle is 11 years younger than Mikhail. The sum of their ages is 77 What is Mikhail's age?

Answer 1

Gabrielle : 33

Mikhail : 44

Step-by-step explanation:

Let Mikhail's age be x

And Gabrielle's age be y.

======================

Gabrielle is 11 years younger than Mikhail

y = x - 11 [ equation 1 ]

sum of their ages is 77

x + y = 77 [ equation 2 ]

Insert equation 1 into 2

x + x - 11 = 77

2x = 77 + 11

2x = 88

x = 44

Therefore, the age of Mikhail is 44

Find Gabrielle's age:

y = x - 11

y = 44 - 11

y = 33

Therefore, the age of Gabrielle is 33

Answer 2

44

Step-by-step explanation:

The relations can be written using one variable to represent Mikhail's age: m. Gabrielle's age is (m-11), so the sum of their ages is ...

m +(m -11) = 77

2m = 88 . . . . . . add 11

m = 44 . . . . . . . divide by 2

Mikhail's age is 44.

__

Additional comment

Gabrielle is 33.

You could solve this using two variables:

• m - g = 11
• m + g = 77

Adding these two equations gives the one we have above:

2m = 88

m = 44

__

You may have noticed we are given the sum and the difference of the two ages. The older Mikhail's age is half the sum of those two numbers. The younger Gabrielle's age is half their difference: (77 -11)/2 = 33. This "half the sum, half the difference" solution is the generic solution to a "sum and difference" problem.