# number problems help please (algebra)

• Jan 19th 2010, 01:06 PM
sri340
1)
The numerator of a fraction is 1 less than the denominator. if the numerator and the denominator are both increased by 4 ,the new fraction will be 1/8 more than the original fraction . find the original fraction

2)
the sum of two numbers is 10 and the sum of their reciprocals is 5/12 . find the numbers

3)
two numbers differ by 11 .when the larger number is divided by the smaller, the quotient is 2 and the remainder is 4. find the numbers
• Jan 19th 2010, 01:14 PM
pickslides
All these problems require you to set up a system of equations to solve.

Read the problem carefully and determine what can be done.

Quote:

Originally Posted by sri340

2)
the sum of two numbers is 10 and the sum of their reciprocals is 5/12 . find the numbers

Let's call your 2 numbers $\displaystyle x$ and $\displaystyle y$.

From the first sentence in the problem $\displaystyle x+y = 10$

From the second sentence $\displaystyle \frac{1}{x}+\frac{1}{y}= \frac{5}{12}$

From the first equation $\displaystyle x = 10-y$ which in turn changes the second equation into

$\displaystyle \frac{1}{10-y}+\frac{1}{y}= \frac{5}{12}$

Can you solve it from here?