Kyle works at a donut factory, where a 10-oz cup of coffee costs 95cents, a 14-oz cup costs $1.15, and a 20-oz cup costs
$1.50. During one busy period, Kyle served 26 cups of coffee, using 384 ounces of coffee, while collecting a total of $31.40. How many cups of each size did Kyle fill?
Let x = no. of 10 oz cups sold Let y = no. of 14 oz cups sold Let z = no. of 20 oz cups sold : Equation 1: total number of cups sold: x + y + z = 24 : Equation 2: amt of coffee consumed: 10x + 14y + 20z = 384 : Equation 3: total revenue from cups sold .95x + 1.15y + 1.50z = 30.60 : Mult the 1st equation by 20 and subtract the 2nd equation from it: 20x + 20y + 20z = 480 10x + 14y + 20z = 384 ------------------------ subtracting eliminates z 10x + 6y = 96; (eq 4)
Mult the 1st equation by 1.5 and subtract the 3rd equation from it: 1.5x + 1.5y + 1.5z = 36.00 .95x + 1.15y+ 1.5z = 30.60 ---------------------------subtracting eliminates z again .55x + .35y = 5.40; (eq 5)
Multiply eq 4 by .055 and subtract from eq 5: .55x + .35y = 5.40 .55x + .33y = 5.28 --------------------eliminates x 0x + .02y = .12 y = .12/.02 y = 6 ea 14 oz cups sold
Substitute 6 for y for in eq 4 10x + 6(6) = 96 10x = 96 - 36 x = 60/10 x = 6 ea 10 oz cups
That would leave 12 ea 20 oz cups (24 - 6 - 6 = 12)
Check our solutions in eq 2: 10(6) + 14(6) + 20(12) = 60 + 84 + 240 = 384 oz
A lot steps, hope it made some sense! I hope this helps!! ;D
