The length of a rectangle was reduced by 10% and the width by x%. If the resulting dimensions reduced the area by 32.5%, what is the value of x?
A) 25
B) 21
C) 18
D) 13
I don’t know what to do at all.
the area LW is changed to
(.90L)(1 - x/100)W = 0.675LW
.9(1-x/100)=0.675
1-x/100 = 0.75
x/100 = .25
x = 25
or, you could just have said
.9*z=.675
z=.75
so the width was 75% of its original size
so, (A)
Well, let me try to help you solve this riddle, I mean, problem! So, we have a rectangle and its length is reduced by 10%. That means it's now only 90% of its original length. As for the width, it is reduced by x%. So, its width is now 100% - x% of its original width.
Now, the area of a rectangle is given by length multiplied by width. If both the length and width are reduced, the new area will be the original area multiplied by the reduction in length and width.
So, if the resulting dimensions reduced the area by 32.5%, we can set up the equation:
(90%/100%) multiplied by (100% - x%/100%) = 67.5%/100%
Simplifying that, we get:
0.9 * (1 - x/100) = 0.675
Dividing both sides by 0.9, we have:
1 - x/100 = 0.75
Now, let's solve for x:
x/100 = 1 - 0.75
x/100 = 0.25
x = 0.25 * 100
x = 25
So, it looks like the value of x is 25. Therefore, the answer is A) 25.
I hope that helps, and if it doesn't, at least I provided some clowny entertainment along the way!
To solve this problem, let's break it down step by step:
1) Let's assume the original length of the rectangle is L and the original width is W.
2) The length is reduced by 10%, which means the new length is 90% of L, or 0.9L.
3) The width is reduced by x%, so the new width is (100 - x)% of W, or (100 - x)/100 * W.
4) The original area of the rectangle is A = L * W.
5) The new area of the rectangle is A' = (0.9L) * (100 - x)/100 * W.
6) The new area is reduced by 32.5%, which means the new area is 67.5% of the original area:
A' = (67.5/100) * A
7) Substitute the values for A and A' from step 4 and 6 into the equation:
(0.9L) * (100 - x)/100 * W = (67.5/100) * (L * W)
8) Simplify the equation:
0.9 * (100 - x) = 67.5
9) Solve for x:
90 - 0.9x = 67.5
-0.9x = 67.5 - 90
-0.9x = -22.5
x = -22.5 / -0.9
x = 25
Therefore, the value of x is 25.
To solve this problem, let's start by understanding the given information:
1. The length of the rectangle was reduced by 10%.
2. The width of the rectangle was reduced by x%.
3. The resulting dimensions reduced the area by 32.5%.
Now, let's break down the problem step by step:
1. Let's assume the original length of the rectangle is L, and the original width is W.
2. After reducing the length by 10%, the new length becomes (L - 0.1L) = 0.9L.
3. After reducing the width by x%, the new width becomes (W - (x/100)W) = (1 - (x/100))W.
Now, let's calculate the area of the rectangle using the original and new dimensions:
Original Area = L * W
New Area = (0.9L) * (1 - (x/100))W
We know that the new area is reduced by 32.5%, which means the new area is equal to 67.5% of the original area:
New Area = 0.675 * Original Area
Substituting the values of the original and new areas, we have:
(0.9L) * (1 - (x/100))W = 0.675 * (L * W)
Next, let's cancel out common factors:
0.9 * (1 - (x/100)) = 0.675
Now, solve for x:
0.9 - (0.9 * (x/100)) = 0.675
Rearrange the equation:
(0.9 * (x/100)) = 0.9 - 0.675
Simplify:
(0.9x/100) = 0.225
Multiply both sides by 100:
0.9x = 22.5
Divide both sides by 0.9:
x = 22.5 / 0.9
x ≈ 25
Therefore, the value of x is approximately 25.
So, the correct option is A) 25.