Here are the solutions to the problems:
16.
Step 1: Let M be the total amount of money.
The problem states that 43 of the money is 36000 frs.
So, we can write the equation:
43M=36000
Step 2: Solve for M.
Multiply both sides by 34:
M=36000×34
M=336000×4
M=12000×4
M=48000
All of the money is worth 48000frs.
17.
Step 1: Identify the number to be rounded.
The number is 3.256.
Step 2: 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≥5, we round up the third significant figure.
So, 5 becomes 6.
The number 3.256 correct to 3 significant figures is 3.26.
18.
Step 1: Calculate the value of each term.
82=8×8=64
32=3×3=9
22=2×2=4
Step 2: Perform the subtraction.
82−32−22=64−9−4
=55−4
=51
The value is 51.
19.
Step 1: Identify the principal amount (P), rate (R), and time (T).
Principal (P) = 72000 frs
Rate (R) = 8% per annum = 0.08
Time (T) = 2 years
Step 2: Use the simple interest formula: I=P×R×T.
I=72000×0.08×2
I=72000×0.16
I=11520
The simple interest is 11520frs.
20.
Step 1: Identify the diameter (d).
Diameter (d) = 14 cm
Step 2: Use the formula for the circumference of a circle: C=πd.
Using π≈722:
C=722×14
C=22×2
C=44
The circumference is 44cm.
21.
Step 1: Write the decimal as a fraction.
0.075=100075
Step 2: 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=3
1000÷25=40
So, the fraction in its lowest terms is 403.
0.075 as a fraction in its lowest term is 403.
22.
Step 1: Calculate the value of each term.
82=8×8=64
32=3×3=9
Step 2: Multiply the results.
82×32=64×9
=576
The value is 576.
23.
Step 1: Identify the average and the number of values.
Average of 3 numbers = 45
Number of values = 3
Step 2: Use the formula: Sum = Average × Number of values.
Sum=45×3
Sum=135
The sum of the three numbers is 135.
24.
Step 1: Identify the total volume and total price.
Total volume of kerosene = 20 liters
Total price = 700 frs
Step 2: Calculate the price per liter.
Price per liter=TotalvolumeTotalprice
=20liters700frs
=35 frs/liter
The price per liter was 35frs.
25.
Step 1: Calculate the total fraction of salary spent.
Spent on food = 53
Spent on rent = 101
Total spent = 53+101
To add these fractions, find a common denominator, which is 10.
53=5×23×2=106
Total spent = 106+101=107
Step 2: Calculate the fraction left for other things.
The whole salary is represented by 1.
Fraction left = 1−Total spent
=1−107
=1010−107
=103
The fraction left for other things is 103.
26.
Step 1: Identify the number.
The number is 72,295.
Step 2: Write the number in words.
The number is Seventy-two thousand, two hundred ninety-five.
In words, 72,295 is Seventy−twothousand,twohundredninety−five.
27.
Step 1: Identify the number.
The number is 2.503.
Step 2: 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 5tenths or 0.5.
28.
Step 1: Identify the given values for the rectangular lawn.
Perimeter (P) = 24 m
Length (L) = 4 m
Step 2: Use the formula for the perimeter of a rectangle: P=2(L+W), where W is the width.
24=2(4+W)
Step 3: Solve for W.
Divide both sides by 2:
224=4+W
12=4+W
Subtract 4 from both sides:
W=12−4
W=8
The width of the lawn is 8m.
29.
Step 1: Add the numbers in base 10.
23+42=65
Step 2: Convert the sum (65 in base 10) to base 5.
Divide 65 by 5 repeatedly and record the remainders.
65÷5=13 remainder 0
13÷5=2 remainder 3
2÷5=0 remainder 2
Read the remainders from bottom to top: 2305.
So, 23+42 in base 5 is 2305.
30.
Step 1: Identify Peter's birth year and the age he will be.
Birth year = 1982
Age = 37 years
Step 2: Add the age to the birth year to find the target year.
Year=1982+37
Year=2019
Peter will be 37 years old in the year 2019.
That's 2 down. 3 left today — send the next one.