# Help required

• Mar 24th 2009, 08:44 AM
shanram74
Help required
A travel agency gives following discounts to their customers as follows:-
0-6 days in advance - 0%
7-13 days in advance- 10%
14-25 days in advance- 25%

A persons pays $1050 for his ticket.Had he purchased the ticket 1 day later, he would have paid$210 more.How many days before did he purchase the ticket?

Can someone help me solve this problem?
• Mar 24th 2009, 09:15 AM
running-gag
Hi

You know that one day after he would not have paid the same price
Therefore he bought his ticket or 7 days or 14 days before

If it is 7 days before then he paid with a 10% decrease (he paid 0.9 time the normal price)
Therefore 0.9 p = 1050 => p = 1050/0.9 = 1166.67
The day after he would have paid the normal price p (because no reduction) which is 1166.67
But you know that he would have paid 210 more than 1050 = 1260
And 1166.67 is not equal to 1260
Therefore the hypothesis is wrong

If it is 14 days before ... your turn !
• Mar 24th 2009, 09:16 AM
Percentages
Hello shanram74
Quote:

Originally Posted by shanram74
A travel agency gives following discounts to their customers as follows:-
0-6 days in advance - 0%
7-13 days in advance- 10%
14-25 days in advance- 25%

A persons pays $1050 for his ticket.Had he purchased the ticket 1 day later, he would have paid$210 more.How many days before did he purchase the ticket?

Can someone help me solve this problem?

Welcome to Math Forum!

If you get a 10% discount, you pay only 90% of the full price. This means that if you pay $$\displaystyle x, the full price is  \displaystyle \frac{100}{90}x. So could 1050 be 90% of the full price? No, because \displaystyle \frac{100}{90}\times 1050 gives an inexact decimal answer. (Try it and see!) On the other hand, if you get a 25% discount, you pay only 75% of the full price. So this time, if you pay$$\displaystyle x$, the full price is$ $\displaystyle \frac{100}{75}x$. How does this work with $1050? Well,$\displaystyle \frac{100}{75}\times 1050 = 1400$. This is better! So it looks as if the full price is$1400, and he's just managed to get a 25% discount. If he'd been a day later, he'd only have got a 10% discount...

Can you finish it off now?