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The problem states that (3)/(4) of the money is 36000 frs.

Mathematics

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16.

  1. Let MM be the total amount of money.

    The problem states that 34\frac{3}{4} of the money is 36000 frs36000 \text{ frs}.
    So, we can write the equation:

    34M=36000\frac{3}{4} M = 36000
  2. Solve for MM.

    Multiply both sides by 43\frac{4}{3}:

    M=36000×43M = 36000 \times \frac{4}{3} M=36000×43M = \frac{36000 \times 4}{3} M=12000×4M = 12000 \times 4 M=48000M = 48000

    All of the money is worth 48000 frs\boxed{48000 \text{ frs}}.

    17.

  3. Identify the number to be rounded.

    The number is 3.256.

  4. Round to 3 significant figures.

    The first three significant figures are 3, 2, and 5.
    The digit after the third significant figure (5) is 6. Since 6≥56 \ge 5, we round up the third significant figure.
    So, 5 becomes 6.
    The number 3.256 correct to 3 significant figures is 3.26\boxed{3.26}.

    18.

  5. Calculate the value of each term.

    82=8×8=648^2 = 8 \times 8 = 64 32=3×3=93^2 = 3 \times 3 = 9 22=2×2=42^2 = 2 \times 2 = 4
  6. Perform the subtraction.

    82−32−22=64−9−48^2 - 3^2 - 2^2 = 64 - 9 - 4 =55−4= 55 - 4 =51= 51

    The value is 51\boxed{51}.

    19.

  7. Identify the principal amount (PP), rate (RR), and time (TT).

    Principal (PP) = 72000 frs72000 \text{ frs}
    Rate (RR) = 8%8\% per annum = 0.08
    Time (TT) = 2 years2 \text{ years}

  8. Use the simple interest formula

    I=P×R×TI = P \times R \times T.

    I=72000×0.08×2I = 72000 \times 0.08 \times 2 I=72000×0.16I = 72000 \times 0.16 I=11520I = 11520

    The simple interest is 11520 frs\boxed{11520 \text{ frs}}.

    20.

  9. Identify the diameter (dd).

    Diameter (dd) = 14 cm14 \text{ cm}

  10. Use the formula for the circumference of a circle

    C=πdC = \pi d.
    Using π≈227\pi \approx \frac{22}{7}:

    C=227×14C = \frac{22}{7} \times 14 C=22×2C = 22 \times 2 C=44C = 44

    The circumference is 44 cm\boxed{44 \text{ cm}}.

    21.

  11. Write the decimal as a fraction.

    0.075=7510000.075 = \frac{75}{1000}
  12. Simplify the fraction to its lowest terms.

    Divide both the numerator and the denominator by their greatest common divisor.
    Both 75 and 1000 are divisible by 25.

    75÷25=375 \div 25 = 3 1000÷25=401000 \div 25 = 40

    So, the fraction in its lowest terms is 340\frac{3}{40}.
    0.075 as a fraction in its lowest term is 340\boxed{\frac{3}{40}}.

    22.

  13. Calculate the value of each term.

    82=8×8=648^2 = 8 \times 8 = 64 32=3×3=93^2 = 3 \times 3 = 9
  14. Multiply the results.

    82×32=64×98^2 \times 3^2 = 64 \times 9 =576= 576

    The value is 576\boxed{576}.

    23.

  15. Identify the average and the number of values.

    Average of 3 numbers = 45
    Number of values = 3

  16. Use the formula

    Sum = Average ×\times Number of values.

    Sum=45×3\text{Sum} = 45 \times 3 Sum=135\text{Sum} = 135

    The sum of the three numbers is 135\boxed{135}.

    24.

  17. Identify the total volume and total price.

    Total volume of kerosene = 20 liters20 \text{ liters}
    Total price = 700 frs700 \text{ frs}

  18. Calculate the price per liter.

    Price per liter=Total priceTotal volume\text{Price per liter} = \frac{\text{Total price}}{\text{Total volume}} =700 frs20 liters= \frac{700 \text{ frs}}{20 \text{ liters}} =35 frs/liter= 35 \text{ frs/liter}

    The price per liter was 35 frs\boxed{35 \text{ frs}}.

    25.

  19. Calculate the total fraction of salary spent.

    Spent on food = 35\frac{3}{5}
    Spent on rent = 110\frac{1}{10}
    Total spent = 35+110\frac{3}{5} + \frac{1}{10}
    To add these fractions, find a common denominator, which is 10.

    35=3×25×2=610\frac{3}{5} = \frac{3 \times 2}{5 \times 2} = \frac{6}{10}

    Total spent = 610+110=710\frac{6}{10} + \frac{1}{10} = \frac{7}{10}

  20. Calculate the fraction left for other things.

    The whole salary is represented by 1.
    Fraction left = 1−Total spent1 - \text{Total spent}

    =1−710= 1 - \frac{7}{10} =1010−710= \frac{10}{10} - \frac{7}{10} =310= \frac{3}{10}

    The fraction left for other things is 310\boxed{\frac{3}{10}}.

    26.

  21. Identify the number.

    The number is 72,295.

  22. Write the number in words.

    The number is Seventy-two thousand, two hundred ninety-five.
    In words, 72,295 is Seventy-two thousand, two hundred ninety-five\boxed{\text{Seventy-two thousand, two hundred ninety-five}}.

    27.

  23. Identify the number.

    The number is 2.503.

  24. Determine the place value of 5.

    In the number 2.503:
    2 is in the units place.
    5 is in the tenths place.
    0 is in the hundredths place.
    3 is in the thousandths place.
    The value of 5 in the number is 5 tenths\boxed{5 \text{ tenths}} or 0.5\boxed{0.5}.

    28.

  25. Identify the given values for the rectangular lawn.

    Perimeter (PP) = 24 m24 \text{ m}
    Length (LL) = 4 m4 \text{ m}

  26. Use the formula for the perimeter of a rectangle

    P=2(L+W)P = 2(L + W), where WW is the width.

    24=2(4+W)24 = 2(4 + W)
  27. Solve for WW.

    Divide both sides by 2:

    242=4+W\frac{24}{2} = 4 + W 12=4+W12 = 4 + W

    Subtract 4 from both sides:

    W=12−4W = 12 - 4 W=8W = 8

    The width of the lawn is 8 m\boxed{8 \text{ m}}.

    29.

  28. Add the numbers in base 10.

    23+42=6523 + 42 = 65
  29. Convert the sum (65 in base 10) to base 5.

    Divide 65 by 5 repeatedly and record the remainders.
    65÷5=1365 \div 5 = 13 remainder 0
    13÷5=213 \div 5 = 2 remainder 3
    2÷5=02 \div 5 = 0 remainder 2
    Read the remainders from bottom to top: 2305230_5.
    So, 23+4223 + 42 in base 5 is 2305\boxed{230_5}.

    30.

  30. Identify Peter's birth year and the age he will be.

    Birth year = 1982
    Age = 37 years37 \text{ years}

  31. Add the age to the birth year to find the target year.

    Year=1982+37\text{Year} = 1982 + 37 Year=2019\text{Year} = 2019

    Peter will be 37 years old in the year 2019\boxed{2019}.

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