Hao Sheng, his father and his grandfather have an average age of 53. One-half of his grandfather's age, plus one-third of his father's age, plus one-fourth of Hao Sheng's age is 65. If 4 years ago, Hao Sheng's grandfather was four times as old as Hao Sheng, then how old are they now?

---- Hao Sheng

--- His father

---- His grandfather

Step-by-step explanation:

Given

From the question, we have:

--- The average of their age

--- 4 years ago

Required

Their current age

Open bracket

Make z the subject

Multiply by 12

Substitute in

Collect like terms

Substitute in

Multiply through by 3

Collect like terms

Make y the subject

Substitute in

Collect like terms

Divide by 7

Solve for y in

Solve for z in

we know that

applying the law of sines

°

so

∠j=18°

∠k=29°

∠l=180-(18+29)=133°

the answer part a) is

the measure of angle k is  ≈29°

part b)  the measure of angle k could also be

(180-29)=151°

so

∠j=18°

∠k=151°

∠l=180-(18+151)=11°

the answer part b) is

the measure of angle k could also be 151°

read more on -