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Hongfa transportation company has received a task to transport 62 tons of goods from Weihai to Yantai. It is known that large trucks can transport 10 tons each time, and the freight is 200 yuan; small trucks can transport 4 tons each time, and the freight is 90 yuan. Suppose you are the manager of the company, can you design an optimal car rental scheme (that is, the freight is the most economical)?
Because the freight per ton of large trucks is: 200 △ 10 = 20 (yuan) and that of small trucks is: 90 △ 4 = 22.5 (yuan) 20 ＜ 22.5, so it is cheaper to use large trucks as much as possible, while 62 = 50 + 12 = 5 × 10 + 4 × 3, so it needs 5 large trucks and 3 small trucks 5 × 200 + 3 × 90 = 1270 (yuan)
Four large trucks and five small trucks transport 14.5 tons of goods at a time, and 10 small trucks and five large trucks transport 20 tons of goods at a time. What is the load weight of large trucks and small trucks
Let's use the quadratic equation
Let the big card be x and the small card be y;
4X+5Y=14.5 …… ①③④
5X+10Y=20 …… ②
① Equation × 2, we get: 8x + 10Y = 29 ③
③ - 1: 3x = 9
x=3
5×3＋10y=20
10y=5
y=0.5
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