Jack is in a restaurant - Edexcel - GCSE Maths - Question 12 - 2020 - Paper 2
Question 12
Jack is in a restaurant.
There are 5 starters, 8 main courses and some desserts on the menu.
Jack is going to choose one starter, one main course and one dessert.
H... show full transcript
Worked Solution & Example Answer:Jack is in a restaurant - Edexcel - GCSE Maths - Question 12 - 2020 - Paper 2
Step 1
Calculate the total number of combinations
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Answer
To determine if Jack's claim of having 240 combinations is correct, we need to calculate the total number of ways to choose one starter, one main course, and one dessert.
Given:
Number of starters = 5
Number of main courses = 8
Let the number of desserts be represented as d
The total number of combinations can be expressed mathematically as:
extTotalcombinations=extNumberofstartersimesextNumberofmaincoursesimesextNumberofdesserts=5imes8imesd
Thus, we can write the equation as:
5imes8imesd=240
Step 2
Solve for the number of desserts
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Answer
Now we simplify the equation:
First calculate the product of starters and main courses:
5imes8=40
Now substituting this back into our equation gives:
40imesd=240
To find d, we divide both sides by 40:
d=40240=6
Thus, there should be 6 desserts on the menu.
Step 3
Conclusion about Jack's statement
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Answer
Since we found that the number of desserts must be 6 for Jack's claim of 240 combinations to be correct, we can conclude:
Yes, Jack could be correct if there are exactly 6 desserts available on the menu.
