Lara makes birdseed by mixing peanuts and sunflower seeds in a 2:3 ratio. The peanuts costs 3p per 10g and the sunflower seeds cost 9p per 10g. Lara sells the birdseed £1 per 100g portion. How much profit does Lara make on each portion? Give your answer in pence.
Step by step explanation pl tqsm.

Lara will do a profit of 34 pence by 100 grams of birdseed.

Step-by-step explanation:

The given ratio means that there are 2 grams of peanuts and 3 grams of sunflower per each 5 grams of birdseed. Now, we obtain the amount required of peanuts and sunflower for 100 grams of birdseed by simple rule of three:

Peanuts

Sunflower

If we know that 10 grams of sunflower cost 9 pence and 10 grams of sunflower cost 3 pence, then the total cost of production of 100 grams portion:

And the profit done by Lara is:

Lara will do a profit of 34 pence by 100 grams of birdseed.

Regarding #6:

You did well in identifying the possible rational roots.  Like you, I checked out x=3 as a possible root.  The 3 coefficients remaining after that are 1, -4 and 2.

They correspond to the quadratic expression 1x^2 -4x + 2.

We can apply the quadratic formula here.  a=1, b=-4 and c=2.

                  -(-4) plus or minus sqrt( [-4]^2 - 4(1)(2)  )
Then x =
                                              2(1)
              4 plus or minus sqrt(8)           4 plus or minus 2sqrt(2)
or  x =  =  
                            2                                                   2

Then x = 2 plus or minus sqrt(2).

If you wanted, you could check your work here by using synthetic division.  Let the divisor be 2+sqrt(2) and the 3 coefficients    be   1   -4   2.

The remainder should be zero.