Cormac has some sweets in a bag. The sweets are lime flavoured or strawberry flavoured or orange flavoured. In the bag: number of lime : number of strawberry : number of orange flavoured sweets : 9 : 4 : x Cormac is going to take at random a sweet from the bag. The probability that he takes a lime flavoured sweet is $rac{3}{7}$. Work out the value of x.

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Cormac has some sweets in a bag - Edexcel - GCSE Maths - Question 11 - 2022 - Paper 1

Question 11

Cormac has some sweets in a bag. The sweets are lime flavoured or strawberry flavoured or orange flavoured. In the bag: number of lime : number of stra... show full transcript

Worked Solution & Example Answer:Cormac has some sweets in a bag - Edexcel - GCSE Maths - Question 11 - 2022 - Paper 1

Step 1

Set up the ratio of sweets

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Answer

The given ratio of sweets is 9:4:x. We can express the total number of sweets as:

$ext{Total sweets} = 9 + 4 + x = 13 + x$

Step 2

Calculate the probability

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Answer

The probability of selecting a lime flavoured sweet is given by the fraction of lime sweets to the total:

$P( ext{lime sweet}) = \frac{9}{13 + x}$

According to the problem, this probability equals $rac{3}{7}$ .

Step 3

Solve the equation

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Answer

Setting the equations equal gives:

$\frac{9}{13 + x} = \frac{3}{7}$

Cross-multiplying to eliminate the fractions:

$9 \times 7 = 3 \times (13 + x)$

This simplifies to:

$63 = 39 + 3x$

Now, isolate x:

$63 - 39 = 3x$

$24 = 3x$

Dividing both sides by 3:

$x = 8$

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