Kyle works at a donut​ factory, where a​ 10-oz cup of coffee costs 95¢​, a​ 14-oz cup costs​ $1.15, and a​ 20-oz cup costs​ $1.50. During on

Question

Kyle works at a donut​ factory, where a​ 10-oz cup of coffee costs 95¢​, a​ 14-oz cup costs​ $1.15, and a​ 20-oz cup costs​ $1.50. During one busy​ period, Kyle served 21 cups of​ coffee, using 294 ounces of​ coffee, while collecting a total of ​$24.35. How many cups of each size did Kyle​ fill?
Kyle filled ___ 10-oz cup(s), ___ 14-oz cup(s), and ___ ​20-oz cup(s).

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Thu Nguyệt 4 years 2021-08-17T02:54:12+00:00 1 Answers 5 views 0

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  1. thucuc
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    2021-08-17T02:55:29+00:00
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    kyle works at a donut shop, where a 10oz. cup of coffee costs 95c, a 14 oz. cup of coffee costs $1.15, and a 20oz. cup costs $1.50. during one busy period Kyle served 24 cups of coffee, using 384 ounces of coffee, while collecting a total of $30.60. 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

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