Algebra Test Questions

Date: 1/25/96 at 19:26:10
From: DR MARK B VECCHIO
Subject: algebra

I am studying for exams and need some help solving some problems.

1. Find 3 consecutive integers such that the sum of the first and 
third is 84.

2. The length of a rectangle is 5 less than twice the width, the 
perimeter of the rectangle is 80; find the dimensions of the 
rectangle.

3. c + 2/5 = 3/7

4. 1/6 = a + 3/a-4

I would like to know how to work these out! 

Thanks - Middle school student

Date: 1/27/96 at 21:22:10
From: Doctor Ken
Subject: Re: algebra

Hello!

As DR MARK B VECCHIO wrote to Dr. Math,
>
>1. Find 3 consecutive integers such that the sum of the first and 
>third is 84.

Try this: let x be the first number, x+1 be the second, and x+2 be 
the third.  Then x+x+2 = 84.

>2. The length of a rectangle is 5 less than twice the width, the 
>perimeter of the rectangle is 80; find the dimensions of the 
>rectangle.

Translating into equations, we get 
l = 2w - 5
l + l + w + w = 80

>3. c + 2/5 = 3/7

The first step in solving this would be to move the 2/5 over to 
the right side, right?  So you'd get
 c = 3/7 - 2/5.  
Then all you'd have to do is do the subtraction.

>4. 1/6 = a + 3/a-4

What you want to do is get rid of all the fractions, right?  Well, 
you've got a 6 on the bottom of one fraction, and an "a" on the 
bottom of another, so try multiplying through by 6, and then by a, 
and then you can either factor or use the quadratic formula.  How 
fun!

-Doctor Ken,  The Geometry Forum