下图显示了空杯时的质量,以及在杯中放入物体 A、B 和 C 的不同组合时的质量。

  1. (a)

    空杯子的质量是多少?

    答:(a) ___

  2. (b)

    物体 A 的质量是多少?

    答:(b) ___

  3. (c)

    物体 A、B 和 C 的平均质量是多少?

    答:(c) ___

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完整解法

9(a)

1. Read the mass of the empty cup directly from the first bar on the graph

From the graph, the height of the first bar (empty cup) is 70 g70\text{ g}.

答案

70 g70\text{ g}

9(b)

1. Find the combined mass of each pair of objects by subtracting the mass of the empty cup.

Mass of A + B = 280−70=210280 - 70 = 210 g
Mass of A + C = 360−70=290360 - 70 = 290 g
Mass of B + C = 320−70=250320 - 70 = 250 g

2. Find the total mass of A, B, and C, and then find the mass of A.

Sum of the three pairs: 2(A+B+C)=210+290+250=7502(A + B + C) = 210 + 290 + 250 = 750 g
Total mass of A + B + C = 750÷2=375750 \div 2 = 375 g
Mass of A = Total mass - (Mass of B + C) = 375−250=125375 - 250 = 125 g

答案

125125 g

9(c)

1. Find the mass of each pair of objects by subtracting the mass of the empty cup.

Mass of A + B = 280−70=210 g280 - 70 = 210\text{ g}
Mass of A + C = 360−70=290 g360 - 70 = 290\text{ g}
Mass of B + C = 320−70=250 g320 - 70 = 250\text{ g}

2. Sum the masses of the three pairs to find the total mass of A, B, and C.

Sum of the three pairs = 210+290+250=750 g210 + 290 + 250 = 750\text{ g}
Since each object is counted twice in this sum:
2×(Mass of A + B + C)=750 g2 \times (\text{Mass of A + B + C}) = 750\text{ g}
Total mass of A, B and C=750÷2=375 g\text{Total mass of A, B and C} = 750 \div 2 = 375\text{ g}

3. Calculate the average mass of the three objects.

Average mass=3753=125 g\text{Average mass} = \frac{375}{3} = 125\text{ g}

答案

125 g125\text{ g}

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