How to construct linear equations Q2b) Q11 and Q13?

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I've found the formula for a which is #r=(v+mu)/(m+1)#. But I could construct equation for c without getting a bizarre answer. enter image source here
For questions 11, I got the equation 10x+5(41-2x)=205 but x=0 in this case.

And lucky last questions 13
I did x=Apollo y=aph and z=ad
Z=x+7200 y=x-4000
So we have x+x+7200-400=303200
And go x=98800, complete different to the answer. Can't someone please correct my mistake? And I will love you forever:)

1 Answer
Feb 6, 2017

Answer:

2(b) #m=v/u#
(11) We have #10# pieces of length #12m# and #5# pieces of length #17m#.
(13) Mr. Aphrodite earn #$96000#, Mr. Apollo earns #$100000# and Mr. Adonis earns #$107200#

Explanation:

2(b)

As #1/v+1/u=2/r#, we have #1/v-1/r=1/r-1/u#

or #(r-v)/(vr)=(u-r)/(ru)#

i.e. #(r-v)/(u-r)=(vr)/(ru)=v/u#

or #m=(v-r)/(r-u)=v/u#

(11) let there be #10# pieces of length #x# and #5# pieces of length #y#.

As total length is #205m#, we have #10x+5y=205# or dividing by #5#

#2x+y=41# ..................(A)

Further, as three pieces of size #x# exceed two pieces of size #y# by #2#, we have

#3x-2y=2# ..................(B)

Now multiplying (A) by #2# and adding to (B), we get

#4x+2y+3x-2y=82+2# i.e. #7x=84# and #x=12#

and putting this in (A) we get #2xx12+y=41# or ##24+y=41#

i.e. #y=41-24=17#

Hence, we have #10# pieces of length #12# and #5# pieces of length #17#.

(13)

Let Mr. Aphrodite earn #x#, then Mr. Apollo earns #x+$4000# and Mr. Adonis earns #(x+$4000)+$7200# or #x+$11200#

As their total earnings are #$303200#, we have

#x+x+4000+x+11200=303200#

or #3x+15200=303200#

or #3x=303200-15200=28800#

and #x=288000/3=96000#

Hence, Mr. Aphrodite earn #$96000#, then Mr. Apollo earns #$96000+$4000=$100000# and Mr. Adonis earns #$100000+$7200# or #$107200#.