Q:

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