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25 January, 12:30

A bakery gave out coupons to celebrate its grand opening. Each coupon was worth either $1, $3, or $5. Twice as many $1 coupons were given out as $3 coupons, and 3 times as many $3 coupons were given as $5 coupons. The total value of all the coupons given out was $360. How many $3 coupons were given out?

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  1. 25 January, 12:39
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    54

    $3 dollar coupons were given

    Step-by-step explanation:

    We can represent this question as a system of equations

    Let

    x = number of $1 dollar coupons

    y = number of $3 dollar coupons

    z = number of $5 dollar coupons

    Twice as many $1 coupons were given out as $3 coupons,

    x = 2*y

    3 times as many $3 coupons were given as $5 coupons.

    y = 3*z

    The total value of all the coupons given out was $360

    x*$1 + y*$3 + z*$5 = $ 360

    The system results

    x - 2y + 0 = 0 (1)

    0 + y - 3z = 0 (2)

    x + 3*y + 5*z = $ 360 (3)

    We substitute equation (2) and (1) into (3)

    (2y) + 3*y + 5 * (y/3) = $ 360

    20*y/3 = 360

    y = 54
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