Question

Hi Maths lovers, if someone can explain me when l want to get NR doing NSR way ( going upwards) where this 3/5 b + 2/5 a or 2/5 a + 3/5 b comes from? Thanks

Answer 1

see explanation

Explanation:

SQ = SP + PQ = - b + a

Since SN : NQ = 3 : 2 then SQ = 3 + 2 = 5 parts , thus

SN =
`(3)/(5)` SQ =
`(3)/(5)` ( - b + a) = -
`(3)/(5)`b +
`(3)/(5)` a

Thus

NR = NS + SR

= - (-
`(3)/(5)` b +
`(3)/(5)` a) + a

=
`(3)/(5)` b -
`(3)/(5)` a + a

=
`(2)/(5)` a +
`(3)/(5)` b

Answer 2

Yeah

Explanation:

Very simple

It was said that

SN:NQ=3:2

→2SN = 3NQ

SN=SR-NR

SN=a - NR

NQ = NR - QR

NQ=NR - b

SQ = SN + NQ

Recall that SN=(3NQ)/2

SQ = (3NQ)/2 + NQ

SQ = (5/2)NQ

a - b = (5/2)(NR - b)

After simplification

NR = (2/5)a - (2/5)b +b

Factorize

NR = (2/5)a + (-2/5 + 1)b

NR = (2/5)a + (3/5)b