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Solve the following problems: a) Find the amount of money in an account after 5 years if $4,000 FRS is deposited at an annual interest rate of 6.09% compounded quarterly. b) If 12 men working 8 hours

Mathematics

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3 parts
a

5400.44 FRS\text{5400.44 FRS}

b

6 hours per day\text{6 hours per day}

c

122,500 tickets\text{122,500 tickets}

Step-by-step solution

10 steps

Here are the solutions to your homework problems:

Part a· 4 steps

To find the amount of money in the account after 5 years, we use the compound interest formula.

  1. Identify the given values.

    Principal P=4,000P = 4,000 FRS
    Annual interest rate r=6.09%=0.0609r = 6.09\% = 0.0609
    Number of times interest is compounded per year n=4n = 4 (quarterly)
    Time t=5t = 5 years

  2. Apply the compound interest formula A=P(1+rn)ntA = P\left(1 + \frac{r}{n}\right)^{nt}.

    A=4000(1+0.06094)4×5A = 4000\left(1 + \frac{0.0609}{4}\right)^{4 \times 5}

  3. Calculate the value inside the parenthesis and the exponent.

    A=4000(1+0.015225)20A = 4000(1 + 0.015225)^{20} A=4000(1.015225)20A = 4000(1.015225)^{20}

  4. Calculate the final amount.

    A=4000×1.35011A = 4000 \times 1.35011 A=5400.44A = 5400.44

    The money in the account after 5 years will be 5400.44 FRS\boxed{\text{5400.44 FRS}}.

Part b

6 hours per day\text{6 hours per day}

This is an inverse proportion problem involving men, hours, and days.

  1. Calculate the total work units for the first scenario.

    Work units = Men ×\times Hours/day ×\times Days
    Work units =12 men×8 hours/day×10 days=960 man-hours-days= 12 \text{ men} \times 8 \text{ hours/day} \times 10 \text{ days} = 960 \text{ man-hours-days}

  2. Set up the equation for the second scenario, where the total work units remain the same.

    Let H2H_2 be the hours per day for 20 men to finish in 8 days.
    20 men×H2 hours/day×8 days=960 man-hours-days20 \text{ men} \times H_2 \text{ hours/day} \times 8 \text{ days} = 960 \text{ man-hours-days}

  3. Solve for H2H_2.

    160×H2=960160 \times H_2 = 960 H2=960160H_2 = \frac{960}{160} H2=6H_2 = 6

    20 men must work 6 hours per day\boxed{\text{6 hours per day}}.

Part c

122,500 tickets\text{122,500 tickets}

To find the total number of tickets available, we use percentages.

  1. Identify the given information.

    Tickets sold = 98,000
    This represents 80% of the total available tickets.

  2. Set up the equation.

    Let TT be the total number of tickets.

    80% of T=98,00080\% \text{ of } T = 98,000 0.80×T=98,0000.80 \times T = 98,000

  3. Solve for TT.

    T=98,0000.80T = \frac{98,000}{0.80} T=122,500T = 122,500

    The total number of tickets that were available for the tournament is 122,500 tickets\boxed{\text{122,500 tickets}}.

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