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50 sweets weigh 200 g - OCR - GCSE Maths - Question 15 - 2019 - Paper 1

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50 sweets weigh 200 g. If each sweet weighs the same, work out the weight of 7 sweets. (b) b is directly proportional to a. b is 10 when a is 8. Work out b when a... show full transcript

Worked Solution & Example Answer:50 sweets weigh 200 g - OCR - GCSE Maths - Question 15 - 2019 - Paper 1

Step 1

If each sweet weighs the same, work out the weight of 7 sweets.

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Answer

To find the weight of one sweet, we divide the total weight by the number of sweets:

Weight of one sweet=200 g50=4 g\text{Weight of one sweet} = \frac{200 \text{ g}}{50} = 4 \text{ g}

Now, to find the weight of 7 sweets:

Weight of 7 sweets=7×4 g=28 g\text{Weight of 7 sweets} = 7 \times 4 \text{ g} = 28 \text{ g}

Step 2

Work out b when a is 9.

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Answer

Since b is directly proportional to a, we can express this relationship as:

b=k⋅ab = k \cdot a

Where k is the constant of proportionality. We know from the problem that when a is 8, b is 10, so:

10=k⋅8  ⟹  k=108=1.2510 = k \cdot 8 \implies k = \frac{10}{8} = 1.25

Now, substituting k into the equation to find b when a is 9:

b=1.25⋅9=11.25b = 1.25 \cdot 9 = 11.25

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