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Solve the following problems: 1. Solve for x: 2x − 1 = 11. 2. Convert ₵45.62 to pesewas. 3. Calculate the amount paid after a 30% discount on ₵200. 4. Solve for x: 2 x 9 = 648. 5. Calculate the perime

Mathematics

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12 steps
  1. Solve the linear equation for xx.

    2x−1=112x - 1 = 11

    Add 1 to both sides:

    2x=11+12x = 11 + 1 2x=122x = 12

    Divide by 2:

    x=122x = \frac{12}{2} x=6x = 6

    The value of xx is 6\boxed{6}.

  2. Convert ₵45.62 to pesewas.

    Assuming "bo" is a typo for "pesewas" and ₵1 = 100 pesewas.

    45.62 Cedi×100pesewasCedi=4562 pesewas45.62 \text{ Cedi} \times 100 \frac{\text{pesewas}}{\text{Cedi}} = 4562 \text{ pesewas}

    ₵45.62 is equal to 4562 pesewas\boxed{4562 \text{ pesewas}}.

  3. Calculate the amount paid after a discount.

    Original cost = ₵200
    Discount = 30%
    Discount amount = 30%30\% of ₵200

    0.30×200=600.30 \times 200 = 60

    Discount amount = ₵60
    Amount paid = Original cost - Discount amount

    200−60=140200 - 60 = 140

    The buyer will pay ₵140\boxed{₵140}.

  4. Solve for xx.

    Assuming the equation is 2×x×9=6482 \times x \times 9 = 648.

    18x=64818x = 648

    Divide by 18:

    x=64818x = \frac{648}{18} x=36x = 36

    The value of xx is 36\boxed{36}.

  5. Calculate the perimeter of the rectangular field.

    Length (LL) = 100 m
    Breadth (WW) = 50 m
    Perimeter (PP) = 2(L+W)2(L + W)

    P=2(100 m+50 m)P = 2(100 \text{ m} + 50 \text{ m}) P=2(150 m)P = 2(150 \text{ m}) P=300 mP = 300 \text{ m}

    The perimeter of the rectangular field is 300 m\boxed{300 \text{ m}}.

  6. Calculate the perimeter of the rhombus.

    A rhombus has four equal sides. Assuming the side length is 5 cm (taking the first value given, as "5cm by 8cm" is contradictory for a rhombus).
    Side length (ss) = 5 cm
    Perimeter (PP) = 4s4s

    P=4×5 cmP = 4 \times 5 \text{ cm} P=20 cmP = 20 \text{ cm}

    The perimeter of the rhombus is 20 cm\boxed{20 \text{ cm}}.

  7. Find the cost price.

    Selling Price (SP) = ₵14
    Profit = 40%
    Let Cost Price (CP) be xx.
    SP = CP + Profit
    SP = CP + (Profit % of CP)

    14=x+0.40x14 = x + 0.40x 14=1.40x14 = 1.40x

    Divide by 1.40:

    x=141.40x = \frac{14}{1.40} x=10x = 10

    The cost price is ₵10\boxed{₵10}.

  8. Simplify the ratio.

    Ratio = 18:45
    Find the greatest common divisor (GCD) of 18 and 45.
    Factors of 18: 1, 2, 3, 6, 9, 18
    Factors of 45: 1, 3, 5, 9, 15, 45
    The GCD is 9.
    Divide both parts of the ratio by 9:

    189:459\frac{18}{9} : \frac{45}{9} 2:52 : 5

    The ratio in its lowest term is 2:5\boxed{2:5}.

  9. Calculate C's share.

    Total amount = ₵48
    Ratio A:B:C = 2:3:5
    Total ratio parts = 2+3+5=102 + 3 + 5 = 10
    C's share = C’s ratio partTotal ratio parts×Total amount\frac{\text{C's ratio part}}{\text{Total ratio parts}} \times \text{Total amount}

    C’s share=510×48\text{C's share} = \frac{5}{10} \times 48 C’s share=12×48\text{C's share} = \frac{1}{2} \times 48 C’s share=24\text{C's share} = 24

    C's share is ₵24\boxed{₵24}.

  10. Calculate the number of years.

    Principal (P) = ₵800
    Amount (A) = ₵960
    Interest (I) = A - P = ₵960 - ₵800 = ₵160
    Interest Rate (R) = 5% per annum = 0.05
    Simple Interest formula: I=P×R×TI = P \times R \times T

    160=800×0.05×T160 = 800 \times 0.05 \times T 160=40×T160 = 40 \times T

    Divide by 40:

    T=16040T = \frac{160}{40} T=4T = 4

    The money was in the bank for 4 years\boxed{4 \text{ years}}.

  11. Convert Cedi to Pounds.

    Assuming the conversion rate is £1 = ₵300.
    Amount in Cedi = ₵27,000
    Amount in Pounds = Amount in CediCedi per Pound\frac{\text{Amount in Cedi}}{\text{Cedi per Pound}}

    Amount in Pounds=27000300\text{Amount in Pounds} = \frac{27000}{300} Amount in Pounds=90\text{Amount in Pounds} = 90

    You could get £90\boxed{£90}.

  12. Find the profit or loss.

    Cost Price (CP) = ₵75
    Selling Price (SP) = ₵63
    Since SP < CP, there is a loss.
    Loss = CP - SP

    75−63=1275 - 63 = 12

    The loss is ₵12\boxed{₵12}.

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