The product of the ages of 4 elementary school students is 5040. A is older than B by a year. B is older than C by a year. C is older than D by a year. What are the ages of the students?

The age of student A = 10 year.

The age of student B=9 years.

The age of student C=8 years.

The age of student D=7 years.

Explanation:

Given:

The product of the ages of 4 elementary school students is 5040.

A is older than B by a year.

B is older than C by a year.

C is older than D by a year.

To find:

The ages of the students?

Solution:

Now, let the age of D be x,

Then, age of C will be x + 1.

Consequently, age of B and A will be x + 2 and x + 3

Now, we know that, product of ages = 5040

x (x + 1) (x + 2) (x + 3) = 5040

x (x + 1) (x + 2) (x + 3) = 504 x 10 [ factorizing the number 5040 ]

x (x + 1) (x + 2) (x + 3) = 84 x 6 x 10

x (x + 1) (x + 2) (x + 3) = 21 x 4 x 6 x 10

x (x + 1) (x + 2) (x + 3) = 7 x 3 x 4 x 3 x 2 x 10

x (x + 1) (x + 2) (x + 3) = 7 x (4 x 2) x (3 x 3) x 10

x (x + 1) (x + 2) (x + 3) = 7 x 8 x 9 x 10

x (x + 1) (x + 2) (x + 3) = 7 (7 + 1) (7 + 2) (7 + 3)

So, by comparison x = 7.

Then, ages of A, B, C, D are 7 + 3 = 10, 7 + 2 = 9, 7 + 1 = 8 and 7 respectively.

Hence, the ages of students are 10 years, 9 years, 8 years, and 7 years for A, B, C, D respectively.