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Joan wants to share R1 245,00 in the ratio 2:3 between Thabo and Valois. Calculate: 1.4.1 How much will Thabo get. 1.4.2 How much will Valois get.

Mathematics

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let's calculate these ratios.

1.1 Simplify the following ratios:

1.1.1

  1. Write the ratio.

    108:56108 : 56
  2. Find the greatest common divisor (GCD) of 108 and 56.

    Factors of 108: 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108.
    Factors of 56: 1, 2, 4, 7, 8, 14, 28, 56.
    The GCD is 4.

  3. Divide both parts of the ratio by the GCD.

    108÷4:56÷4=27:14108 \div 4 : 56 \div 4 = 27 : 14

    The simplified ratio is 27:14\boxed{27:14}.

    1.1.2

  4. Write the ratio.

    150:180150 : 180
  5. Find the greatest common divisor (GCD) of 150 and 180.

    Factors of 150: 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, 150.
    Factors of 180: 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 180.
    The GCD is 30.

  6. Divide both parts of the ratio by the GCD.

    150÷30:180÷30=5:6150 \div 30 : 180 \div 30 = 5 : 6

    The simplified ratio is 5:6\boxed{5:6}.

    1.2 Write the following as unit ratios:

    1.2.1

  7. Write the ratio.

    8:328 : 32
  8. To express as a unit ratio, divide both sides by the first term (8).

    8÷8:32÷8=1:48 \div 8 : 32 \div 8 = 1 : 4

    The unit ratio is 1:4\boxed{1:4}.

    1.2.2

  9. Write the ratio.

    15:11515 : 115
  10. To express as a unit ratio, divide both sides by the first term (15).

    15÷15:115÷15=1:1151515 \div 15 : 115 \div 15 = 1 : \frac{115}{15}
  11. Simplify the fraction 11515\frac{115}{15} by dividing both numerator and denominator by their GCD, which is 5.

    115÷515÷5=233\frac{115 \div 5}{15 \div 5} = \frac{23}{3}

    The unit ratio is 1:233\boxed{1:\frac{23}{3}}.

    1.3
    A new green colour of paint is made by mixing blue paint and yellow paint in the ratio 4:34:3. If you have 12 litres of blue paint, how many litres of yellow paint do I need to make up the new green colour?

  12. Set up the ratio of blue paint to yellow paint.

    Blue paintYellow paint=43\frac{\text{Blue paint}}{\text{Yellow paint}} = \frac{4}{3}
  13. Substitute the given amount of blue paint (12 litres) into the ratio.

    12Y=43\frac{12}{Y} = \frac{4}{3}
  14. Solve for YY (yellow paint).

    4Y=12×34Y = 12 \times 3 4Y=364Y = 36 Y=364Y = \frac{36}{4} Y=9Y = 9

    You need 9 litres\boxed{9 \text{ litres}} of yellow paint.

    1.4 Joan wants to share R1 245,00 in the ratio 2:3 between Thabo and Valois.

    1.4.1 How much will Thabo get?

  15. Calculate the total number of parts in the ratio.

    Total parts=2+3=5\text{Total parts} = 2 + 3 = 5
  16. Determine Thabo's share as a fraction of the total.

    Thabo’s share=25\text{Thabo's share} = \frac{2}{5}
  17. Calculate the amount Thabo will receive.

    Thabo’s amount=25×R1245.00\text{Thabo's amount} = \frac{2}{5} \times \text{R}1245.00 Thabo’s amount=R498.00\text{Thabo's amount} = \text{R}498.00

    Thabo will get R498.00\boxed{\text{R}498.00}.

    1.4.2 How much will Valois get?

  18. Determine Valois's share as a fraction of the total.

    Valois’s share=35\text{Valois's share} = \frac{3}{5}
  19. Calculate the amount Valois will receive.

    Valois’s amount=35×R1245.00\text{Valois's amount} = \frac{3}{5} \times \text{R}1245.00 Valois’s amount=R747.00\text{Valois's amount} = \text{R}747.00

    Alternatively, subtract Thabo's amount from the total:

    Valois’s amount=R1245.00−R498.00=R747.00\text{Valois's amount} = \text{R}1245.00 - \text{R}498.00 = \text{R}747.00

    Valois will get R747.00\boxed{\text{R}747.00}.

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