The teacher gave three students the same amount of money to buy stationery. A bought 3 pens and has $3 left. B bought 5 crayons and has $5 left. C bou

The teacher gave three students the same amount of money to buy stationery. A bought 3 pens and has $3 left. B bought 5 crayons and has $5 left. C bought 7 pencils and has $3 left. If the price for each item is an integer, what is the least total amount of money the teacher gave them?

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  1. Let the price of each type of pens purchased by A,B,C be a,b,c respectively $

    =>3a+3=5b+5=7c+3

    => the amount the teacher gives to each student is divisible by 3 and 5

    => the amount is in the form of 15k

    there are 15≡1(mod 7)

    =>15k≡k(mod 7) where 15k divided by 7 leaves a remainder of 3

    =>k smallest is k=3

    => total amount is 15.3.3=135

    Cho mình câu trả lời hay nhất nhé!

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  2. Let the price of each type of pens purchased by A,B,C be a,b,c respectively $

    =>3a+3=5b+5=7c+3

    => the amount the teacher gives to each student is divisible by 3 and 5

    => the amount is in the form of 15k

    there are 15≡1(mod 7)

    =>15k≡k(mod 7) where 15k divided by 7 leaves a remainder of 3

    =>k smallest is k=3

    => total amount is 15.3.3=135

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