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At a gift shop, the number of $2 gift packs, $5 gift packs and $10 gift packs were in the ratio of 16:9:7. 1/8 of the $2 gift packs and 34 of the $5 gift packs were sold. The remaining gift packs were worth $1975. How many of the $10 gift packs were there?

 May 10, 2022
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Let No. of $2 gift packs = 16x

      No. of $5 gift packs = 9x

      No. of $10 gift packs = 7x

1/8 of $2 gift packs = 1/8 * 16x = 2x.

Total gift packs = 16x + 9x + 7x

                         = 32x

Total sold gift packs = 1/8 of $2 and 34 of $5

                                = (8x + 34)

     remaining gift packs = Total - Sold

                                      = 32x - (8x + 34)

                                      = (30x - 34)

Remaining gift packs -----> $2 ---> 14x

                                           $5 ---> 9x - 34

                                           $10 ---> 7x

        Value of $2 gift box = (14x * 2) = $28x

        Value of $5 gift box = 5(9x - 34) = $(45x - 170)

        Value of $10 gift box = 10(7x) = $70x

      Total remaining value = $(28x + 45x - 170 + 70x)

                     1975            = (143x - 170) dollars

                         2145 = 143x

                      => x = 15

   No. of $10 gift packs = 7x

                                     = 7 * 15

   No. of $10 gift packs = 105

 May 10, 2022

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