Question

【典型例题】a certain project requires petroleum asphalt with a softening point of 85°c. currently, there are two types available: no. 10 and no. 60. how should they be mixed to meet the projects requirements?【例题解答】according to the test results, the softening point of no. 10 petroleum asphalt is 95°c; the softening point of no. 60 petroleum asphalt is 45°c. estimate the mixing quantities of the two types of asphalt.

Explanation:

Step1: Set up the equation

Let the proportion of No. 10 asphalt be \(x\), then the proportion of No. 60 asphalt is \(1 - x\). The equation for the softening point is \(95x+45(1 - x)=85\).

Step2: Expand and simplify the equation

Expand \(95x + 45-45x=85\), then \(50x=85 - 45\).

Step3: Solve for \(x\)

\(50x = 40\), so \(x=\frac{40}{50}=0.8\). Then \(1 - x=1 - 0.8 = 0.2\).

Answer:

The proportion of No. 10 asphalt is \(0.8\) and the proportion of No. 60 asphalt is \(0.2\).