SOLUTION: Two positive numbers have a difference of 17. The larger number is one more than twice the smaller. Find the two numbers. A farmer has 162 feet of fence with which to make a co

Algebra ->  Rectangles -> SOLUTION: Two positive numbers have a difference of 17. The larger number is one more than twice the smaller. Find the two numbers. A farmer has 162 feet of fence with which to make a co      Log On


   

Question 969458: Two positive numbers have a difference of 17. The larger number is one more than twice the smaller. Find the two numbers.
A farmer has 162 feet of fence with which to make a corral. If he arranges it into a rectangle that is twice as long as it is wide, what are the dimensions?
Answer by erica65404(394) About Me  (Show Source):
You can put this solution on YOUR website!
Problem 1:

Two positive numbers have a difference of 17. The larger number is one more than twice the smaller. Find the two numbers.

Step 1:
write equations given the information.

x-y=17
where x is the first positive number and y is the second positive number.

x=2y%2B1
x has to be the larger number because the answer is a positive number
(if x were smaller than y, the answer would be negative, for example: 10-20=-10)

I will break it up into parts

The larger number is one more than twice the smaller.
The larger number: x
is: =
one more than: +1
twice the smaller number: 2y
This combined will give you the equation x=2y%2B1

Step 2:
solve equations

start with the first equation x-y=17
solve for x
x=17%2By

now you can plug in 17%2By for all the x's in the other equation.


x=2y%2B1
17%2By=2y%2B1

now you can solve for y

17%2By=2y%2B1
16%2By=2y
16=y

The smaller number is 16.

To find the bigger number plug 16 into our first equation

x-y=17
x-16=17
x=33

The 2 positive numbers are 33 and 16.

Problem 2:

A farmer has 162 feet of fence with which to make a corral. If he arranges it into a rectangle that is twice as long as it is wide, what are the dimensions?

Step 1:

Make equations given the information.

The perimeter of a rectangle is P=2L%2B2W.
we will use this equation
162=2x%2B2y
where 162 is the length of the fencing available which is also the perimeter of the coral.
x is the length and y is the width.

a rectangle that is twice as long as it is wide
This can be translated into
x=2y

twice as long as it is wide suggests that the length (x) is going to equal (=) 2 times the width (2y)

Step 2:
solve

now that you have 2 equations you can solve for one of the variables.

x=2y
You can plug 2y into any place in the other equation that has x.

162=2x%2B2y
162=2%282y%29%2B2y
162=4y%2B2y
162=6y
27=y

The width is 27.
Now plug in 27.

162=2x%2B2y
162=2x%2B2%2827%29
162=2x%2B54
108=2x
54=x

The length is 54 and the width is 27.
*notice that the length is twice the width.
you can also check your answer to make sure you didn't make any mistakes in your calculations
162=2x%2B2y
162=2%2854%29%2B2%2827%29
162=108%2B54
162=162
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If you have questions, please email me at ericahigley@yahoo.com.