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March 30, 2017

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There are 36 pupils in a class. Each girl is given 8 books and each boy is given 3 books. The total number of books the girls receive is 46 more than the total number of books the boys receive. How many girls are there in the class?

The ratio of the number of boys to that of girls in Class A is 2:3. The ratio of the number of girls who wear glasses to the number of girls who do not wear glasses is 1:3. If there are 12 more girls than boys, how many girls wear glasses?

The average height of 3 girls is 150cm. The heights of two of them are 1.6 m and 1.47 m. What is the height of the third girl?

A regular tank 40cm by 20cm by 20cm is filled with water up to 2/5 of its height. Water from a tap flows into the tank at 2.5 liters a minute. How much water is in the tank after 3 minutes? Give your answer in liters. (1Liter= 1000cm3)

  • Maths - ,

    GB = 8*G
    BB = 3*B
    GB - BB = 46

    Where GB is the number of girl's books, BB is the number of boy's books, G is the number of girls, and B is the number of boys.

    Use algebra to solve this system of equations

    2nd problem

    B/G = 2/3
    G(glasses) + G(noglasses) = G
    G(glasses)/G(noglasses) = 1/3
    G - B = 12

    where B is number of boys, G is number of girls, G(glasses) is number of girls with glasses, G(noglasses) is number of girls without glasses

    Use algebra to solve this system of equations

    3rd question:

    1.6 m = 160 cm; 1.47 m = 147 cm

    (160 + 147 + x) / 3 = 150

    where x is the height of the third girl. Solve for x

    4th question

    The water in the tank before the tap turns on is

    2/5 * 40 * 20 * 20 = 3200 cm3 = 3.2 L

    After three minutes, 2.5 * 3 = 7.5 L

    The total amount of water in the tank is 3.2 L + 7.5 L

  • Maths - ,

    1. number of girls ---- x
    number of boys --- 36-x

    8x - 3(36-x) = 46
    8x - 108 + 3x = 46
    11x = 154
    x = 14

    There are 14 girls in the class

    2. number of boys = 2x
    number of girls = 3x
    1/4 of the girls wear glasses, or
    (3/4)x girls wear glasses

    "there are 12 more girls than boys" ---> x - (36-x) = 12
    2x = 48
    x = 24

    There are 24 girls , and 1/4 of those wear glasses
    Then 6 girls wear glasses

    check:
    24 girls and 12 boys, ratio is 12:24 = 2:3 , checks
    1/4 of the 24 girls wear glasses ---> 6 girls wear glasses
    ratio of glassed girl to non-glassed girls = 6 : 18 = 1:3 , checks
    All is good!


    3. (x+1.6+1.47)/3 = 1.50
    x+1.6+1.47 = 4.5
    x = 1.43

    Third girl is 1.43 m or 143 cm tall

    4. rate of flow = 2.5 L/min
    after 3 minutes new amount of water = 3(2.5) = 7.5 L
    plus the (2/5)(40)(20)(20) or 6400 mc^3 or 6.4 L already in tank
    gives us 13.91 L

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