Manchester grammar school paper 2016

[brimoyuyu]

Can anyone please help on questions 12 and 20? So I can explain them to my son

12. Rachel buys three identical bags of sweets and 5 cans of drink, the total cost of these items came to £4.90. Rosie buys just one bag of sweets and three cans of drink and pays £2.70. What is the cost of a bag of sweets?

83 is a prime number. If Nancy reverses the order of the digits she gets 38 which is not prime. How many two digit primes do give a different prime number when their digits are reversed?
Thanks

[Guest55]

12. Rachel buys three identical bags of sweets and 5 cans of drink, the total cost of these items came to £4.90. Rosie buys just one bag of sweets and three cans of drink and pays £2.70. What is the cost of a bag of sweets?

I would avoid using algebra ...

First bit of info: three bags of sweets and 5 cans of drink, cost £4.90
Second bit: one bag of sweets and three cans of drink cost £2.70 so if we triple this [to get the same amount of sweets]
..................three bags of sweets and 9 cans cost £8.10

So you shoud be able to see how to get the cost of 4 cans, then divide to get one and them work out the sweets.

Or you could make the same number of cans ..

[Guest55]

83 is a prime number. If Nancy reverses the order of the digits she gets 38 which is not prime. How many two digit primes do give a different prime number when their digits are reversed?

OK a bit of thinking needed about primes - they can't be even so that eliminates any primes that are 20s, 40s, 60s or 80s.

So try the others 11, 13, 17 etc and see

[brimoyuyu]

Thanks a lot Guest55.
It's so clear now.
Really appreciate your help

[russet]

Primes: you only need to check odd, non 5 endings in tens, thirties and seventies. By the nineties, you will have checked all except 99 and any number which repeats is non prime, except 11.
So that leaves 13, 17, 19, 37, 39 and 79 to check.

[brimoyuyu]

Thanks russet

[Guest55]

Primes: you only need to check odd, non 5 endings in tens, thirties and seventies. By the nineties, you will have checked all except 99 and any number which repeats is non prime, except 11.

Surely it's quicker to just check the primes in the range?