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Mrac [35]
2 years ago
7

10. The average age of 4 boys is 14 years, when one boy leaves the group, the average age of the remaining boys becomes 15 years

. How old is the 4th boy?​
Mathematics
1 answer:
Hatshy [7]2 years ago
3 0

Answer: the 4th boy is 11

Step-by-step explanation:

Let's denote the age of the boys as: x₁, x₂, x₃, x₄.

Then,

\displaystyle\\\frac{x_1+x_2+x_3}{3}=15

Multiply both parts of the equation by denoting by 3:

x₁+x₂+x₃=15(3)

x₁+x₂+x₃=45

Hence,

\displaystyle\\\frac{x_1+x_2+x_3+x_4}{4} =14\\\\\frac{(x_1+x_2+x_3)+x_4}{4} =14\\\\\frac{45+x_4}{4}=14

Multiply both parts of the equation by denoting by 4:

45+x₄=14(4)

45+x₄=56

45+x₄-45=56-45

x₄=11

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