Hannah is (3/7) as heavy as Irna and (3/4) as heavy as Jiahui. What is the ratio of Hannah's mass to the total mass of the 3 girls?
taking the ratios in reverse,
I/H = 7/3
J/H = 4/3
(I+J)/H = 11/3
I+J = 11/3 H
I+J+H = 14/3 H
so, H/(I+J+H) = 3/14
the simplest case is that Hannah weighs 3, Irna weighs 7, Jiahui weighs 4
The desired ratio is thus 3/(3+7+4) = 3/14
To find the ratio of Hannah's mass to the total mass of the three girls, we need to determine the masses of all three girls first.
Let's assume the total mass of the three girls is represented by a variable, say "M".
Given that Hannah is (3/7) as heavy as Irna, we can express Irna's mass as (7/3) times Hannah's mass. So, Irna's mass is (7/3) * Hannah's mass.
Given that Hannah is (3/4) as heavy as Jiahui, we can express Jiahui's mass as (4/3) times Hannah's mass. So, Jiahui's mass is (4/3) * Hannah's mass.
Now, we can write an equation for the total mass of the three girls:
M = Hannah's mass + Irna's mass + Jiahui's mass
Substituting the expressions for Irna's and Jiahui's mass:
M = Hannah's mass + (7/3) * Hannah's mass + (4/3) * Hannah's mass
Combining like terms:
M = (1 + 7/3 + 4/3) * Hannah's mass
M = (3/3 + 7/3 + 4/3) * Hannah's mass
M = (14/3) * Hannah's mass
To find the ratio of Hannah's mass to the total mass, we divide Hannah's mass by the total mass:
Ratio = Hannah's mass / M
Ratio = Hannah's mass / [(14/3) * Hannah's mass]
Simplifying the expression:
Ratio = 1 / (14/3)
Ratio = 3/14
Therefore, the ratio of Hannah's mass to the total mass of the three girls is 3:14.