Question

How to construct linear equations Q2b) Q11 and Q13?

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.
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:)

Answer 1

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`.