Letts question

[wildwest]

30 people go to a restaurant. All the diners order from the below menu;
Three course meal: £12
Two course meal: £9

If the total bill was £345, how many people ordered a three course meal?

How do I explain the method to DD?

Could anyone please guide me?

[Guest55]

Think about how the answer can end in a 5 in the units ...

[Nicoleyb]

345= 12 a + 9b -----1

where a =no of peeps eating 3 course
B = no peeps eating 2 course


30 people eating therefore a+b = 30 ----------2

Simply simultaneous equations now:

A= 30 - b. subst into equation 1

345= 12(30-b) +9b
345 = 360-12b+9b

15=3b
B= 5

From ------2. 30=a+5

a= 25

Therefore 25 peeps ate a 3 course meal and 5 ate a two course meal

[motion]

DS split 345 into multiples of 9 and 12, and by just looking at number he saw a pattern 300 and 45, and could see 45 is a multiple of 9, (9 x5) and 12 goes into 300 25 times hence, 25 people ordered £12 main course

[wildwest]

Thanks everyone. dd gets it now. not sure if she will be able to apply this in the exam scenario ..tomorrow.