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?
Accepted Solution
A:
Answer:54 $3 dollar coupons were givenStep-by-step explanation:We can represent this question as a system of equationsLet x = number of $1 dollar couponsy = number of $3 dollar couponsz = number of $5 dollar couponsTwice as many $1 coupons were given out as $3 coupons,x = 2*y3 times as many $3 coupons were given as $5 coupons. y = 3*zThe total value of all the coupons given out was $360x*$1 + y*$3 + z*$5 = $ 360The system resultsx - 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) = $ 36020*y/3 = 360y = 54