Question 5
(a) An takes the average of four natural numbers. The first is 12 more than the average, the second is $2/3$ of the average, the third is 19 and the fourth is 25. Find the sum of the first and second numbers.
(b) Mr An buys boxes of cakes. Type A has 4 cakes per box and costs 60,000 đồng per box; type B has 6 cakes and costs 60,000 đồng; type C has 5 cakes and costs 80,000 đồng. He spends 960,000 đồng on 73 cakes. The number of type C boxes is 9 less than the total number of type A and B boxes. How many type A boxes does he buy? Show your reasoning for both parts.
(b) Mr An buys boxes of cakes. Type A has 4 cakes per box and costs 60,000 đồng per box; type B has 6 cakes and costs 60,000 đồng; type C has 5 cakes and costs 80,000 đồng. He spends 960,000 đồng on 73 cakes. The number of type C boxes is 9 less than the total number of type A and B boxes. How many type A boxes does he buy? Show your reasoning for both parts.