Question

The ratio of the ages (in years) of two teachers is 8:9. The sum of their ages is 51. What is the age of each teachers?

Answer 1

To find the ages of two teachers with an age ratio of 8:9 and a combined age of 51, we set up an equation 17x = 51, solve for x to get 3, and then find the individual ages: 24 years for the first teacher, and 27 years for the second teacher.

Step-by-step explanation:

The question asked is a typical algebra problem involving ratios and the sum of two quantities. To solve for the ages of two teachers given the ratio of their ages as 8:9 and the sum of their ages as 51, we first set up two algebraic expressions. Let the age of the first teacher be 8x and the age of the second teacher be 9x. The sum of their ages is given as 51 years.

Therefore, the equation to solve is 8x + 9x = 51. Simplifying this, we combine like terms to get 17x = 51. Dividing both sides of the equation by 17, we find x = 3.

Now, to find the individual ages, we multiply x by the original ratio numbers: The first teacher's age is 8x = 8 * 3 = 24 years, and the second teacher's age is 9x = 9 * 3 = 27 years.

Answer 2

x = 24yrs and y = 27yrs

Step-by-step explanation:

Let the age of one of the teachers be x

Let the age of the other teacher be y

From the second sentence;

x + y = 51 ----------(1)

From the first sentence;

x/y = 8/9 ------------(2)

Making y the subject of formula in equation (1) as follows;

y = 51 -x -------------(3)

Substitute (3) into (2) as follows;

x/51- x = 8/9

Cross multiply as follows:

9*x = 8(51- x)

9x = 408 - 8x

Collecting like terms;

9x + 8x = 408

17x = 408

Divide both sides by 17;

x = 24 yrs

Substitute x = 24 into equation (3) as follows;

y = 51 - 24

y = 27 yrs