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A baker uses (3)/(4) kg of flour, (5)/(6) kg of sugar, and (1)/(3) kg of cocoa. He sells the mixture for GHC 120 per kg. Find the total mass of the mixture and the total sales.

Mathematics

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b)

  1. Add the masses of flour, sugar, and cocoa.

    Mass of flour =34= \frac{3}{4} kg
    Mass of sugar =56= \frac{5}{6} kg
    Mass of cocoa =13= \frac{1}{3} kg
    Total mixture =34+56+13= \frac{3}{4} + \frac{5}{6} + \frac{1}{3} kg

  2. Find the least common multiple (LCM) of the denominators 4, 6, and 3.

    The LCM of 4, 6, and 3 is 12.

  3. Convert each fraction to an equivalent fraction with a denominator of 12 and add them.

    34=3×34×3=912\frac{3}{4} = \frac{3 \times 3}{4 \times 3} = \frac{9}{12} 56=5×26×2=1012\frac{5}{6} = \frac{5 \times 2}{6 \times 2} = \frac{10}{12} 13=1×43×4=412\frac{1}{3} = \frac{1 \times 4}{3 \times 4} = \frac{4}{12}

    Total mixture =912+1012+412=9+10+412=2312= \frac{9}{12} + \frac{10}{12} + \frac{4}{12} = \frac{9 + 10 + 4}{12} = \frac{23}{12} kg

  4. The fraction 2312\frac{23}{12} is already in its simplest form because 23 is a prime number and 12 is not a multiple of 23.

    The total mixture is 2312 kg\boxed{\frac{23}{12} \text{ kg}}.

    c)

  5. Use the total mass from part (b), which is 2312\frac{23}{12} kg.

    Selling price per kg = GHC 120

  6. Calculate the total sales by multiplying the total mass by the selling price per kg.

    Total sales =Total mixture×Price per kg= \text{Total mixture} \times \text{Price per kg}

    Total sales=2312 kg×120 GHC/kg\text{Total sales} = \frac{23}{12} \text{ kg} \times 120 \text{ GHC/kg} Total sales=23×12012 GHC\text{Total sales} = 23 \times \frac{120}{12} \text{ GHC} Total sales=23×10 GHC\text{Total sales} = 23 \times 10 \text{ GHC} Total sales=230 GHC\text{Total sales} = 230 \text{ GHC}

    The total sales are GHC 230\boxed{\text{GHC } 230}.

    1. a)
  7. Express 0.000684 in standard form.

    To move the decimal point after the first non-zero digit (6), we move it 4 places to the right.

    0.000684=6.84×10−40.000684 = 6.84 \times 10^{-4}
  8. Round 6.84×10−46.84 \times 10^{-4} to 3 significant figures.

    The number 6.84 already has 3 significant figures.
    So, 0.000684 in standard form and rounded to 3 significant figures is 6.84×10−4\boxed{6.84 \times 10^{-4}}.

    b)

  9. Solve the equation 2x×8=642^x \times 8 = 64.

    Divide both sides by 8.

    2x=6482^x = \frac{64}{8} 2x=82^x = 8
  10. Express 8 as a power of 2.

    8=238 = 2^3
  11. Substitute this back into the equation.

    2x=232^x = 2^3
  12. Since the bases are the same, equate the exponents.

    x=3x = 3

    The solution is x=3\boxed{x=3}.

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