SOLUTION: Hi The question is A man bought a lot of lemons for £5; for one third he paid 4p a piece; and for the rest 3p a piece. How many lemons did he buy? Thank you

Algebra ->  College  -> Linear Algebra -> SOLUTION: Hi The question is A man bought a lot of lemons for £5; for one third he paid 4p a piece; and for the rest 3p a piece. How many lemons did he buy? Thank you      Log On


   

Question 1112870: Hi
The question is
A man bought a lot of lemons for £5; for one third he paid 4p a piece; and for the rest 3p a piece. How many lemons did he buy?
Thank you
Answer by greenestamps(13203) About Me  (Show Source):
You can put this solution on YOUR website!


For 1/3 of the lemons he paid 4p each, for the other 2/3 he paid 3p each. That means he bought twice as many at 3p each as he bought at 4p each.

So consider "packages" of 1 lemon at 4p and 2 lemons at 3p each. Each of those packages costs 10p, so for £5 he can buy 50 of those packages.

Since there are 3 lemons in each package, the number of lemons he bought was 50*3 = 150.

Algebraically....

Let x be the total number of lemons.
Then he bought (1/3)x lemons at 4p each and (2/3)x lemons at 3p each; and the total cost was £5 = 500p. So

%281%2F3%29x%2A4+%2B+%282%2F3%29x%2A3+=+500
%284%2F3%29x%2B2x+=+500
%2810%2F3%29x+=+500
x+=+500%2A%283%2F10%29+=+150