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19 August, 12:24

Use the three steps to solve the problem. Maple syrup worth $6.00 a gallon and corn syrup worth. 80 cents a gallon are used to make a mixture worth $2.36 a gallon. How many gallons of each kind of syrup are need to make 50 gallons of the mixture?

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Answers (2)
  1. 19 August, 12:45
    0
    15 gallons of maple syrup

    35 gallons of corn syrup

    Step-by-step explanation:

    Firstly, I would like to make all our currency be in cents.

    Let the number of maple syrup needed be m and the number of corn syrup be c.

    Now, the mixture costs 236 cents per mixture. We interpret this using the cost of each syrup to make a mathematical expression as follows:

    600m + 80c = 236 (m + c) ... (i)

    Now we need 50 gallons, meaning, the number of both syrups add up to 50.

    m + c = 50 ... (ii)

    We now solve both equations simultaneously.

    From (i), we can get 364m - 156c = 0

    From (ii) we get c = 50 - m

    If we insert this into that expression from (i), we get

    364m - 156 (50 - m) = 0

    This yields, 520m = 7800

    And m = 15

    Since c = 50 - m,

    Then c = 50 - 15 = 35
  2. 19 August, 12:46
    0
    118

    Step-by-step explanation:

    Let

    a = gallons of $6 syrup

    b = gallons of $ 80 syrup

    then

    equation 1

    a + b = 50

    equation 2

    6a +.8b / 50=2.36

    6a +.8b = 2.36 * 50

    6a +.8b = 118

    multiply equation 3 with 10

    60a + 8b = 1180

    multiplay equation 1 with 8 and then subt 1 from 2

    (2) 60 + 8b = 1180

    (1) - 8a-8b=-400

    52a = 780

    a=15

    and

    a+b = 50

    15 + b=50

    b=35

    15 = gallons of $6 syrup

    35=gallons of $.80

    6a+.8b/50 = 2.36

    6 (15) +.8 (35) / 50 = 2.36

    90 + 28 / 50 = 2.36

    118/50 = 2.36

    118 = 118
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