Mathematics

Question

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1 Answer

  • To solve this I am going to create three equations for what each person bought.
    a will represent apples, b will represent berries, and c will represent cherries.

    34 = 2a + 1b + 4c
    35 = 3a + 2b + 2c
    49 = 5a + 3b + 2c

    Solve for on variable in the first equation.

    b = 34 - 2a - 4c

    Plug that into the second equation and solve for a different variable.

    35 = 3a + 2(34 - 2a - 4c) + 2c
    35 = 3a + 68 - 4a - 8c + 2c
    35 = -a + 68 - 6c
    -33 = -a - 6c
    33 = a +6c
    a = 33 - 6c

    It gets a little confusing here but you plug in what both a and b are equal to until you have solved for c.

    49 = 5a + 3b + 2c
    49 = 5(33 - 6c) + 3b + 2c               substitute a with 33 - 6c
    49 = 165 - 30c + 3b +2c
    49 = 165 - 28c + 3b
    -116 = -28c + 3(34 - 2a - 4c)               substitute b with 34 - 2a - 4c
    -116 = -28c + 102 - 6a - 12c
    -116 = -40c + 102 - 6(33 - 6c)               again substitute a with 33 - 6c
    -116 = -40c + 102 - 198 + 36c
    -116 = -4c - 96
    -20 = -4c
    4c = 20
    c = 5

    a = 33 - 6c
    a = 33 - 6(5)
    a = 33 - 30
    a = 3

    b = 34 - 2a - 4c
    b = 34 - 2(3) - 4(5)
    b = 34 - 6 - 20
    b = 8

    Apples cost $3 per pound
    Berries cost $8 per pound
    Cherries cost $5 per pound