the lenght of a rectangle is 4 feet less than 3 times the width. the sum of the length and width is 14 more th

Question

the lenght of a rectangle is 4 feet less than 3 times the width. the sum of the length and width is 14 more than the width. find the width.

help i don't get it!!! i hate story problems!!

Answer 1

Let L be the length and W be the width.

Then L=3W-4, because the length is 4 ft less than 3 times the width.

Also, L+W=14+W, from the second statement.

From the second statement, cancel the W's, and you get L=14.

Now substitute L=14 into the first equation, and get 14=3W-4, so 3W=18. This means W=6.

Answer 2

If you draw a rectangle and label according to the story you might find these easier.

Since the first sentence tells you about the length, put a w next to the width (or an x if you prefer).

Since the lenght is 4 feet less that 3 times the width, you know you have to multiply the width by 3 (3w) and then it's less than that so subtract 4. Now you have 3w-4 on the length of the rectangle.

You get this information from the first sentence so you will get the equation from the second.

replace the sum of the length and width with 3w-4+w
replace is with an equal sign
replace 14 more than the width with w+14
(think of it as the width plus 14 because if it were less than
you'd have to think of it as the width minus 14)

Now you have 3w-4+w=w+14
combine like terms 4w-4=w+14
subtraxt w from both sides 3w-4=14
Add 4 to both sides 3w=18
Divide both sides by 3 w=6 width is 6 feet
so the length is 3w-4. or 18-4 or 14 length is 14 feet

You didn't have to find the length but I did so that I could show you how You can check your answers.

Is the length 4 feet less than 3 times the width?

Is the sum of the length and the width 14 more than the width?

Answer 3

The second part of the question essentially tells you the length. Allow x to be the width and y to be the length. If the sum of x+y is 14 more than x the equation is as follows:
x+y=x+14
then you subtract x from both sides:
y=14
Therefore the length is 14. The first part of the question gives you enough information to create the equation:
3x-4=y
Since we know that y=14 now we can plug y into the equation:
3x-4=14
Add 4 to both sides:
3x=18
Divide both sides by 3:
x=6
Therefore the width is 6 units.
I hope I helped you!

Answer 4

sum of l and w is w + 14:
l + w = w + 14

length is 3x width - 4:
l = 3w -4

what is width?

solve the first equation for length:
l + w = w + 14
l = w - w + 14
l = 14

now solve the second equation since you know length:
14 = 3w - 4
3w = 14 + 4
3w = 18
w = 6

now, to prove your answer, use the two values in the first equation:
l + w = w + 14
14 + 8 = 8 + 14
22 = 22

Yes, since the values on each side of the equal sign are the same, you have solved the equation correctly.

If you follow the steps as I have laid them out, you will be able to solve many problems! Hopefully you understand the manipulations I did... If not, ask more questions or email me.

Good luck to you!

Answer 5

enable x = the width enable 3x-9 = the length Perimeter = 2L+2W Perimeter = 2(3x-9) + 2x remedy for x 6x-18+2x=206 8x-18=206 8x=224 x=28 The length hence will be 3(28)-9 = seventy 5 and the width will be 28.

Answer 6

use l as the length; use w as the width
a) 3w - 4 = l
b) l + w = w + 14

we can't do much with equation a yet

take away w from each side of equation b
now you have l = 14

for equation a you can now replace l with 14
3w - 4 = 14
3w = 4 + 14
3w = 18
w = 6