Answer:
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.
