Question

Las edades de cuatro hermanos forman una progresión aritmética, y su suma es 32 años. El mayor tiene 6 años más que el menor. Halla las edades de los cuatro hermanos.

Answer 1

The ages of the four siblings are: 5, 7, 9 and 11 years old.

Explanation:

The computation of the age of the four siblings is shown below:

Given that

n = 4

a1 =? a2 =? a3 =? a4 =?

a4 = a1 + 6 years

S4 = 32

Based on the above information

As we know that

Sn = (a1 + a4) × n ÷ 2

S4 = (a1 + a4) × 4 ÷ 2

32 = (a1 + a1 +6) × 2

16 = 2a1 + 6

2a1 = 10

a1 = 10 ÷ 2

= 5

So, a4 = a1 +6

= 5 +6

= 11

a4 = a1 + (4-1) × d

11 = 5 + 3 × d

d = 6 ÷ 3

= 2

So,

a2 = a1 + d

= 5 + 2

= 7

a3 = a2 + d

= 7 + 2

= 9

Hence, The ages of the four siblings are: 5, 7, 9 and 11 years old.