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Question 2: a) The total cost of food and drinks for the month was GH¢733.07. If the cost of food was GH¢477.32, find the cost of drinks. b) i) How much more was budgeted for food than for drinks? ii)

Mathematics

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b) i)

  1. Identify the cost of food and drinks from the table.

    Cost of Food = GH¢477.32
    Cost of Drinks = GH¢255.75

  2. Calculate the difference between the cost of food and drinks.

    Difference=Cost of Food−Cost of Drinks\text{Difference} = \text{Cost of Food} - \text{Cost of Drinks} Difference=GH¢477.32−GH¢255.75\text{Difference} = \text{GH¢}477.32 - \text{GH¢}255.75 Difference=GH¢221.57\text{Difference} = \text{GH¢}221.57

    He budgeted GH¢221.57 more on food than drinks.

    b) ii)

  3. Identify the budgeted amount for drinks.

    Budgeted amount for Drinks = GH¢255.75

  4. Calculate four-fifth of the budgeted amount for drinks.

    Amount spent=45×GH¢255.75\text{Amount spent} = \frac{4}{5} \times \text{GH¢}255.75 Amount spent=0.8×GH¢255.75\text{Amount spent} = 0.8 \times \text{GH¢}255.75 Amount spent=GH¢204.60\text{Amount spent} = \text{GH¢}204.60

    The amount actually spent on drinks is GH¢204.60.

    c)

  5. Find the prime factorization of 105 kg.

    105=3×5×7105 = 3 \times 5 \times 7

  6. Find the prime factorization of 120 kg.

    120=2×60=2×2×30=2×2×2×15=23×3×5120 = 2 \times 60 = 2 \times 2 \times 30 = 2 \times 2 \times 2 \times 15 = 2^3 \times 3 \times 5

  7. Find the greatest common divisor (GCD) of 105 and 120.

    The common prime factors are 3 and 5.

    GCD(105,120)=31×51=15\text{GCD}(105, 120) = 3^1 \times 5^1 = 15

    The greatest quantity he can sell the rice in equal amounts is 15 kg.

    d)

  8. Let the actual price of the bicycle be PP.

    The discount is 8%.
    The price paid is the actual price minus the discount.

    Price paid=P−(0.08×P)\text{Price paid} = P - (0.08 \times P) Price paid=P(1−0.08)\text{Price paid} = P(1 - 0.08) Price paid=0.92P\text{Price paid} = 0.92P

  9. We are given that Aku paid GH¢368.00.

    0.92P=GH¢368.000.92P = \text{GH¢}368.00

  10. Solve for PP.

    P=GH¢368.000.92P = \frac{\text{GH¢}368.00}{0.92} P=GH¢400.00P = \text{GH¢}400.00

    The actual price of the bicycle is GH¢400.00.

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