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Math Help - solving equations

  1. #1
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    solving equations

    Pls help...pls show me the steps to solve the following probs...thanks lots..

    Qn1: Limin bought 2.5 metres of cloth. Each dress used
    metres. If she made 3 dresses, how much cloth
    was left?

    Qn2: The ratio of men to women in a food court is 4:3. The ratio
    of women to children is 5:2. If there are 24 children, how
    many men are there?

    Qn3: of Limin's money can buy 40 books. How many books
    can she buy with of her money?
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    Quote Originally Posted by Bryan View Post
    Qn1: Limin bought 2.5 metres of cloth. Each dress used \frac34 metres. If she made 3 dresses, how much cloth
    was left?
    I'll do this first one completely:

    One dress uses \frac34 meters of cloth, so three dresses will use 3\cdot\frac34 = \frac94 meters. So if she started with 2.5 = \frac52 meters of cloth, she will have

    \frac52 - \frac94 = \frac{10}4 - \frac94 = \frac14

    meters of cloth remaining.


    Quote Originally Posted by Bryan View Post
    Qn2: The ratio of men to women in a food court is 4:3. The ratio
    of women to children is 5:2. If there are 24 children, how
    many men are there?
    Let the number of men, women, and children, be m, w,\text{and }c, respectively.

    Then we know that \frac mw = \frac43 and that \frac wc = \frac52.

    But you also know that c = 24. Substitute this into the second relation, and you can solve for the number of women. Then substitute that back into the first equation and you will be able to solve for the number of men.

    Quote Originally Posted by Bryan View Post
    Qn3: \frac25 of Limin's money can buy 40 books. How many books
    can she buy with \frac34 of her money?
    We will have to assume that these books are all the same price. Let that price be c.

    Suppose Limin has x units of money (dollars, pounds, euros, whatever--makes no difference here). Then we know that two-fifths of this amount will total to the cost of 40 books: \frac{2x}5 = 40c.

    Solving for x: x = 40c\cdot\frac52 = 100c. Now, \frac34 of her money will buy n books: \frac{3x}4 = nc. Substitute for x and solve for n.

    (Of course, if you wanted to be picky, the initial relation should actually be 40c\le\frac{2x}5; the answer should work out the same)
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