Translation to English:
A rice supplier mixes three different types of rice into three different blends; Type A, Type B, and Type C.
He blends 1 kg of type A, 2 kg of type B, and 4 kg of type C and sells the blend for IDR 19500
He also blends 2 kg of type A and 3 kg of type B and sells the blend for IDR 19000
The third blend consists of 1 kg of type B and 1 kg of type C and this blend is sold for IDR 6250
Which type of rice is the most expensive?
Solution:
Start with the third blend:
1 kg of type B + 1 kg of type C = 6250
B + C = 6250
B = 6250 - C
Then move on to the second blend:
2 kg of type A + 3 kg of type B = 19000
2A + 3B = 19000
2A + 3(6250 - C) = 19000
2A + 18750 - 3C = 19000
2A - 3C = 19000 - 18750
2A - 3C = 250
2A = 250 + 3C
A = [250 + 3C] / 2
Then move on to the first blend:
1 kg of type A + 2 kg of type B + 4 kg of type C = 19500
A + 2B + 4C = 19500
⇒ Multiply each term by 2
B + C = 6250
B + 1964.3 = 6250
B = 6250 - 1964.3
B = 4285.7
A = [250+C] /2
A = [250 + 1964.3] / 2
A = 1107.15
The most expensive rice is type B
A rice supplier mixes three different types of rice into three different blends; Type A, Type B, and Type C.
He blends 1 kg of type A, 2 kg of type B, and 4 kg of type C and sells the blend for IDR 19500
He also blends 2 kg of type A and 3 kg of type B and sells the blend for IDR 19000
The third blend consists of 1 kg of type B and 1 kg of type C and this blend is sold for IDR 6250
Which type of rice is the most expensive?
Solution:
Start with the third blend:
1 kg of type B + 1 kg of type C = 6250
B + C = 6250
B = 6250 - C
Then move on to the second blend:
2 kg of type A + 3 kg of type B = 19000
2A + 3B = 19000
2A + 3(6250 - C) = 19000
2A + 18750 - 3C = 19000
2A - 3C = 19000 - 18750
2A - 3C = 250
2A = 250 + 3C
A = [250 + 3C] / 2
Then move on to the first blend:
1 kg of type A + 2 kg of type B + 4 kg of type C = 19500
A + 2B + 4C = 19500
B + C = 6250
B + 1964.3 = 6250
B = 6250 - 1964.3
B = 4285.7
A = [250+C] /2
A = [250 + 1964.3] / 2
A = 1107.15
The most expensive rice is type B