The graph below shows the mass of a cup when empty and when different combinations of objects A, B and C are placed in the cup.

  1. (a)

    What is the mass of the empty cup?

    Ans: (a) ___

  2. (b)

    What is the mass of object A?

    Ans: (b) ___

  3. (c)

    What is the average mass of objects A, B and C?

    Ans: (c) ___

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Worked solution

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}.

Answer

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

Answer

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}

Answer

125 g125\text{ g}

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