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Liam makes 32 chocolate biscuits and 40 ginger biscuits. He puts the biscuits into boxes. Each box contains the same number of chocolate biscuits and the same number of ginger biscuits.

a) Find the largest possible number of boxes.

b) Work out the number of chocolate biscuits and the number of ginger biscuits in each box.



Answer :

GinnyAnswer
Sure, let's work through this step by step.

### a) Finding the Largest Possible Number of Boxes

To determine the largest possible number of boxes, we need to find the greatest common divisor (GCD) of the numbers 32 and 40. The GCD is the largest number that divides both 32 and 40 without leaving a remainder.

Given our numerical results:
- The GCD of 32 and 40 is 8.

So, the largest possible number of boxes Liam can make is 8.

### b) Number of Chocolate Biscuits and Ginger Biscuits in Each Box

Once we know the largest number of boxes (which is 8), we can find out how many biscuits of each type go into each box.

1. Chocolate Biscuits in Each Box:
- Total chocolate biscuits = 32
- Number of boxes = 8
- Number of chocolate biscuits per box = Total chocolate biscuits ÷ Number of boxes = 32 ÷ 8 = 4

So, each box contains 4 chocolate biscuits.

2. Ginger Biscuits in Each Box:
- Total ginger biscuits = 40
- Number of boxes = 8
- Number of ginger biscuits per box = Total ginger biscuits ÷ Number of boxes = 40 ÷ 8 = 5

So, each box contains 5 ginger biscuits.

### Conclusion

a) The largest possible number of boxes Liam can make is 8.

b) Each box will contain 4 chocolate biscuits and 5 ginger biscuits.

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