~Solving inequalities~

Hello everybody :-)

I'm pretty good at Algebra, and always have been... but I am not so great when it comes to word problems.
Here is what I need help with:

>>>
The length of a rectangular yard is 50 ft., and it's perimeter is less than 170 ft. Describe the width of the yard.
>>>

I do know this:
The width is less than 70ft. (because 50*2=100 and 170-100=70)
Therefore, the width is 70/2=35.

Is that all the question wants? Am I supposed to write a compound inequality?

Thanks for any help.

2L + 2 W <170

L + W < 85
50 + W < 85
W < 35
however W can not be less than zero so
0 < W < 35

Hello!

Yes, you're correct in determining that the width of the yard should be less than 70 feet. Since the perimeter of a rectangle is given by the formula P = 2(length + width), you can set up the following inequality:

2(length + width) < 170

Substituting the given length of 50 feet:

2(50 + width) < 170

Now, let's solve the inequality step by step:

1. Distribute the 2:
100 + 2*width < 170

2. Simplify:
2*width < 70

3. Divide both sides by 2 to solve for width:
width < 35

So, the width of the yard must be less than 35 feet.

The final answer is width < 35.

Hello! It seems like you have already made progress in solving the word problem. You correctly determined that the width of the yard is less than 70 ft by considering the perimeter. To further describe the width using a compound inequality, we can express the condition you found.

Since the length of the yard is 50 ft, the perimeter is given by the formula P = 2(length + width). We are given that the perimeter is less than 170 ft, so we can write the inequality as follows:

2(50 + w) < 170

To solve this inequality, we can start by simplifying it:

100 + 2w < 170

Next, we can isolate the variable by subtracting 100 from both sides:

2w < 70

Finally, we can solve for the width by dividing both sides of the inequality by 2:

w < 35

So, the width of the yard is less than 35 ft. Therefore, your initial conclusion of the width being 35 ft is correct.

In summary, you did not need to write a compound inequality in this case since the problem only asked you to describe the width. However, if you were required to write a compound inequality, it would be w < 35, representing that the width is less than 35 ft. Well done on your solution! If you have any further questions or need assistance with anything else, feel free to ask.