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?

Question

Mathematics

Deanna Estes

12 November, 07:21

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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Answers (1)

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Stephanie Harrison · Answer 1

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