Vani her father and her grandfather age have an average of 53. One- half of her grandfather's age plus one - third of her father's age plus one-fourth of vani's age is 65.Fpur years ago if vani's grandfather was four times as old as vani then how old are they all now?
Answers
Answer:
Vani = 24
Father = 51
GrandFather = 84
Step-by-step explanation:
Let say Vani Age = V
Father age = F
Grandfather age = G
Vani her father and her grandfather age have an average of 53
Total Age = 53 * 3 = 159
V + F + G = 159 - eq 1
G/2 + F/3 + V/4 = 65
=> 6G + 4F + 3V = 780 eq 2
G-4 = 4(V -4)
=> G - 4 = 4V - 16
=> G - 4V = -12 - eq 3
Eq2 - 4 * eq 1
2G -V = 144 - eq 4
Eq 4 - 2 * eq 3
=> 7V = 168
=> V = 24
2G - 24 = 144
=> 2G = 168
=> G = 84
24 + 84 + F = 159
=> F = 51
Step-by-step explanation:
V = vaani 's age.l
F = vaani's father's age.
G = vaani's father's father's age (vaani's grandfather's age)
the average of their ages is (V + F + G) / 3 which is equal to 53.
(1/2)G + (1/3)F + (1/4)V = 65
solution is:
V = 24
F = 51
G = 84
you do a lot of substitutions to get the answer.
first thing was to remove the denominator which simplifies future calculations.
(V + F + G) / 3 = 53 becomes V + F + G = 159 after multiplying both sides of the equation by 3.
(1/2)F + (1/3)F + (1/4)V = 65 becomes 6G + 4F + 3V = 780 after multiplying both sides of the equation by 12.
you are given that G - 4 = 4 * (V - 4)(
this means that 4 years ago the grandfather was 4 times as old as the grandson.
from this equation, solve for G to get G = 4V - 12
substitute 4V - 12 for G in the equastion V + F + G = 159 to get:
V+ F + 4V - 12 = 159
ombine like terms to get 5V + F - 12 = 159
add 12 to both sides of the equation to get 5V + F = 171
solve for F to get F = 171 - 5V
you now have:
G = 4V - 12
F = 171 - 5V
substitute for G and F in the equation 6G + 4F + 3V = 780 to get:
6 * (4V - 12) + 4 * (171 - 5V) + 3V = 780
simplify to get 24V - 72 + 684 - 20V + 3V = 780
combine like terms to get 7V + 612 = 780
subtract 612 from both sides of the equation to get 7V = 168
divide both sides of the equation by 7 to get V = 24
since G = 4V - 12, this means that G = 84
since F = 171 - 5V, this means that F = 51
that gets you:
V = 24
F = 51
G = 84