Question

if $560 is shared in the ratio 2:3:9, the difference between the largest and the smallest share is

Answer 1

Answer:

y=80 and 360, which difference returns 360–80=280

PREMISES

y=the difference between the largest and smallest terms of 560 divided in the ratio 2:3:9

CALCULATIONS

Let the equality between two ratios be a “proportion” i.e., a:b::c:d, where : stands for “is to” or “divided by” and where :: stands for “as” or “is proportionate to”.

Since the terms in the ratio 2:3:9 add to 14, then the value being divided (560) should be divisible by a fraction of 14

Hence,

2/14(560):3/14(560):9/14(560)

(2×560)/14:(3×560)/14:(9×560)/14

1120/14:1680/14:(5040)/14

80 (smallest term):120:360 (largest term)

y=360–80

y=

280

PROOF

If y=80 and 360, then the inequalities

80<120<360 prove the solution y=80, 360 to the smallest and largest terms of 560 divided in the ratio 2:3:9. 80+120+360=560.

C.H.