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Cormac has some sweets in a bag - Edexcel - GCSE Maths - Question 13 - 2022 - Paper 1
Question 13
Cormac has some sweets in a bag. The sweets are lime flavoured or strawberry flavoured or orange flavoured. In the bag: number of lime flavoured sweets : number of... show full transcript
Worked Solution & Example Answer:Cormac has some sweets in a bag - Edexcel - GCSE Maths - Question 13 - 2022 - Paper 1
Step 1
number of lime flavoured sweets : number of strawberry flavoured sweets : number of orange flavoured sweets = 9 : 4 : x
Answer
Let the total number of sweets in the bag be represented as ( T = 9 + 4 + x = 13 + x ).
The probability of selecting a lime flavoured sweet is given by: [ P(lime) = \frac{number \ of \ lime \ sweets}{total \ number \ of \ sweets} = \frac{9}{T} = \frac{9}{13 + x}. ]
According to the problem, this probability equals ( \frac{3}{7} ): [ \frac{9}{13 + x} = \frac{3}{7}. ]
Cross multiplying gives: [ 9 \times 7 = 3 \times (13 + x) ] [ 63 = 39 + 3x. ]
Subtract 39 from both sides: [ 63 - 39 = 3x ] [ 24 = 3x. ]
Finally, divide both sides by 3: [ x = 8. ]