Question

Richard and Teo have a combined age of 31. Richard is 10 years older than twice​ Teo's age. How old are Richard and​ Teo?

Answer 1

Richard is 24 years old and Teo is 7 years old.

Explanation:

Let's use variables to represent the ages of Richard and Teo.

Let's call Richard's age "R"

Let's call Teo's age "T"

From the problem, we know that:

R + T = 31 (the combined age of Richard and Teo is 31)

R = 2T + 10 (Richard is 10 years older than twice Teo's age)

We can use substitution to solve for one of the variables. From the second equation, we can see that R is equal to 2T + 10, so we can substitute 2T + 10 for R in the first equation:

(2T + 10) + T = 31

Simplifying and solving for T:

3T + 10 = 31

3T = 21

T = 7

So Teo is 7 years old. To find Richard's age, we can substitute T = 7 into the equation R = 2T + 10:

R = 2(7) + 10 = 24

Therefore, Richard is 24 years old and Teo is 7 years old.

Answer 2

We can assume age of Richard is x years and the Age of teo is y years.

If Richard is 10 years older than twice Teo's age Their ages will be,

• Richard's age = 10 + 2y
• Teo's age = y

Since, Richard and Teo have a combined age of 31,

• 10 + 2y + y = 31
• 10 + 3y = 31
• 3y = 31 - 10
• 3y = 21
• y = 21/3
• y = 7

Since, Richard's age is 10 + 2y and teo's age is y. Put the value of y here,

Richard's age =

• = 10 + 2 y
• = 10 + 2 × 7
• = 10 + 14
• = 24 years

Teo's age =

• = y
• = 7 years