Question

1. The cost of producing x hundred litres of olive oil
is 20 + 5x dollars. If the revenue from the sale of
x hundred litres of the oil is 1.5x2 dollars, calculate
to the nearest litre, the number of litres that must
be sold to make a profit of $800.

2. The cost of hiring a chainsaw
is $10 plus an amount that is
proportional to the square of
the number of hours for which
the chainsaw is hired. If it costs
$32.50 to hire the chainsaw for
3 hours, find, to the nearest half
hour, the length of time for which
the chainsaw was hired if the cost
of hire was $60.

3. The sum of the first n whole numbers is equal to the sum of two parts, one of
which varies as n and the other varies as n2.
a) Using k1 and k2 as the constants of proportionality for each part, write down an
expression for the sum S in terms of n.
b) By calculating the sum of the first 4 whole numbers and the sum of the first
5 whole numbers, find the values of k1 and k2.
c) If the sum of the first n whole numbers is equal to 1275, what is the
value of n?

Answer 1

You gonna do any of the work here?

#1.
profit = revenue - cost
They gave you the formulas for both, so just plug and chug:

1.5x^2 - (20 + 5x) = 800

Remember that x is 100 liters

#2. Just start with what they tell you:
c = 10 + kh^2
32.50 = 10 + k*3^2 -- find k.
Then use that to solve for h in
60 = 10+kh^2

#3. Recall that the sum of the first n whole numbers is s = n(n+1)/2
So, now you are told that
s = a+b where
a = k1*n
b = k2*n^2
That is,
n(n+1)/2 = k1*n + k2*n^2
See where that takes you