maths F1

'Good Harvest' (GH) Rice is composed of 50% Chinese rice and 50% Japanese rice, The cost of Chinese rice is $6 per kg. if the manufacture sets the price of a 5 kg GH Rice bag at $60, he can make a profit of 60%.
(a) (i) Find the cost of a bag of GH Rice.
Cost of a bag of GH Rice
= 60/(1+60%)
= $37.5
(ii) Find the cost of Japanese rice per kg.
Let $x be the cost of the Japanese rice per kg,
5(50%)(6)+5(50%)x = 37.5
15 + 2.5x = 37.5
2.5x = 22.5
x = 9
Hence, cost of the Japanese rice per kg is $9.
(b) The cost of Japanese rice is suddenly increased by 50% while the cost of Chinese rice remains unchanged. The manufacturer wants to change the composition of the GH Rice so as to keep its original price, as well as a 60% profit. How many kg of Chinese rice are there in a 5 kg GH Rice bag now?
Let there are x kg of Chinese rice in the bag now, i.e. there are (5-x)kg of Japanese rice in the bag now,
New cost of Japanese rice = 9*50% = $13.5/kg
x * 6 + (5-x) * 13.5 = 37.5
6x + 67.5 - 13.5x = 37.5
-7.5x = -30
x = 4
Hence, there are 4kg of Chinese rice in the bag now