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Mathematics

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Here are the solutions to the math problems.

Question 2.3 Step 1: Determine the total number of parts in the ratio. Total parts =3+2=5= 3 + 2 = 5

Step 2: Calculate the number of learners per part. Learners per part =TotallearnersTotalparts=1255=25= \frac{Total learners}{Total parts} = \frac{125}{5} = 25 learners

Step 3: Calculate the number of learners who jog. Number of joggers =3×25=75= 3 \times 25 = 75 learners

Step 4: Calculate the number of learners who cycle. Number of cyclists =2×25=50= 2 \times 25 = 50 learners

Joggers:75learners,Cyclists:50learners\boxed{Joggers: 75 learners, Cyclists: 50 learners}


Question 2 (Tractor problem) Step 1: Calculate the amount to be financed after the deposit. Loan principal (P)=TractorpriceDeposit(P) = Tractor price - \text{Deposit} P=R160000R20000=R140000P = R160\,000 - R20\,000 = R140\,000

Step 2: Convert the loan period from months to years. Time (t)=60months12months/year=5 years(t) = \frac{60 months}{12 months/year} = 5 \text{ years}

Step 3: Calculate the simple interest. Simple Interest (I)=P×r×t(I) = P \times r \times t I=R140000×0.10×5I = R140\,000 \times 0.10 \times 5 I=R70000I = R70\,000

Step 4: Calculate the total amount paid for the loan (principal + interest). Amount to repay =P+I= P + I Amounttorepay=R140000+R70000=R210000Amount to repay = R140\,000 + R70\,000 = R210\,000

Step 5: Calculate the total amount paid, including the deposit. Total amount paid =Deposit+Amount to repay= Deposit + \text{Amount to repay} Totalamountpaid=R20000+R210000=R230000Total amount paid = R20\,000 + R210\,000 = R230\,000

R230000\boxed{R230\,000}


Question 3.1.1 Step 1: Calculate the product of 4-4 and 33. Product =(4)×3=12= (-4) \times 3 = -12

Step 2: Calculate the sum of 4-4 and 33. Sum =(4)+3=1= (-4) + 3 = -1

Step 3: Subtract the product from the sum. Result =SumProduct= Sum - \text{Product} Result=(1)(12)Result = (-1) - (-12) Result=1+12Result = -1 + 12 Result=11Result = 11

11\boxed{11}


Question 3.1.2 Step 1: Convert the fraction to a decimal. 58=0.625\frac{5}{8} = 0.625

Step 2: Multiply the decimal by 100%100\% to express it as a percentage. 0.625×100%=62.5%0.625 \times 100\% = 62.5\%

62.5%\boxed{62.5\%}


Question 3.1.3 Step 1: Set up the given equation. 37=12A\frac{3}{7} = \frac{12}{A}

Step 2: Cross-multiply to solve for AA. 3×A=7×123 \times A = 7 \times 12 3A=843A = 84

Step 3: Divide by 33 to find the value of AA. A=843A = \frac{84}{3} A=28A = 28

28\boxed{28}

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