Question

Hello,
Please help me with the following :
A man bought a certain number of chairs for 10000. He kept 1 for his own use and sold the rest at a rate of more than 50 he gave for one chair. Besides getting his own chair for nothing, he made a profit of 450 . How chairs did he buy?

regards
Nikita

Answer 1

Let n = number of chairs purchased
p = price paid per chair

np = 10,000

so p=10,000/n

(n-1)(p+50)=10450 (since the total amount earned=10000+450)

np+50n-p-50=10450

np=10000

10000+50n-(10000/n)-50=10450

Subtract 10,000 from both sides and add 50 to both sides. Add 50n and 10,000/n by using n as the common denominator.

(50n^2 - 10000)/n = 500

50n^2 - 10000 = 500n

50n^2 - 500n - 10000 =0

n^2 - 10n - 200 = 0

(n-20)(n+10)=0

n=20 and n=-10

Can't use -10 because there can't be a negative number of chairs. The answer is 20. ​​​​​

Hope this would help.