# Math Help - solving equations

1. ## 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?

2. Originally Posted by Bryan
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.

Originally Posted by Bryan
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.

Originally Posted by Bryan
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)