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Algebra Difficulty 3.3 AMC 10/12 Find the answer

A store had 100 kilograms of vegetables in stock. In the morning, 50 kilograms were sold at a price of 1.2 yuan per kilogram. At noon, 30 kilograms were sold at a price of 1 yuan per kilogram. In the afternoon, 20 kilograms were sold at a price of 0.8 yuan per kilogram. What was the average selling price per kilogram for these vegetables?

A number or a short expression. Spacing and $ signs are ignored.

Solution

To find the average selling price per kilogram for these vegetables, we calculate the total revenue from selling the vegetables and divide it by the total weight of the vegetables sold.

The revenue from selling 50 kilograms in the morning at 1.2 yuan per kilogram is 50×1.2=6050 \times 1.2 = 60 yuan.

The revenue from selling 30 kilograms at noon at 1 yuan per kilogram is 30×1=3030 \times 1 = 30 yuan.

The revenue from selling 20 kilograms in the afternoon at 0.8 yuan per kilogram is 20×0.8=1620 \times 0.8 = 16 yuan.

Therefore, the total revenue from selling all the vegetables is 60+30+16=10660 + 30 + 16 = 106 yuan.

Since the total weight of the vegetables sold is 100 kilograms, the average selling price per kilogram is 106100=1.06\frac{106}{100} = 1.06 yuan.

Thus, the average selling price per kilogram for these vegetables is 1.06\boxed{1.06} yuan.

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Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic and difficulty added by this site.