simultaneous equastions?

Question

If 3 tonne of cement and 1.5 tonne of lime cost £405 and 5 tonne of cement and 1 tonne of lime cost £570 find the cost of a 50kg bag of cement and a 50kg bag of lime
can anyone help with this question

Answer 1

Let c = cost of a tonne of cement
Let L = cost of a tonne of lime
equation one:
3c + 1.5L = 405
equation two:
5c + 1L = 570
rewrite equation two:
L = 570 - 5c
substitute for L in equation one:
3c + 1.5(570-5c) = 405
3c + 885 - 7.5c = 405
885 - 405 = 7.5c - 3c
480 = 4.5c
106.6666 pounds = c
L = 570 -5(106.66...) = 36.66... pounds

A tonne is 1000 kg
A 50kg bag of cement costs (50/1000)*106.6... = 5.333.. pounds
A 50kg bag of lime costs (50/1000)*36.66.. = 1.833... pounds

This all assumes there is no discount for quantity. In the real world, you can buy cement by the tonne for a lower price than you can buy it by the kg.