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Math Help - Help required

  1. #1
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    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?
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  2. #2
    MHF Contributor
    Joined
    Nov 2008
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    France
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    1,458
    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 !
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  3. #3
    MHF Contributor
    Grandad's Avatar
    Joined
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    South Coast of England
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    Percentages

    Hello shanram74
    Quote Originally Posted by shanram74 View Post
    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 $ x, the full price is $ \frac{100}{90}x.

    So could $1050 be 90% of the full price? No, because \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 $ x, the full price is $ \frac{100}{75}x. How does this work with $1050?

    Well, \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?

    Grandad
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