SOLUTION: a homeowner painted her bathroom. she has a mirror that is 30 inches high and 20 inches wide. she decides to decrease both mirror dimensions by the same amount, and she will now ha

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Question 1106090: a homeowner painted her bathroom. she has a mirror that is 30 inches high and 20 inches wide. she decides to decrease both mirror dimensions by the same amount, and she will now have to paint the newly exposed wall. she only has enough paint to cover 225 square inches.
part a says calculate the new area of the mirror
part b says write and solve an equation to find out she should decrease each dimension
i dont understand how to do this
Found 2 solutions by ikleyn, math_helper:
Answer by ikleyn(52794) About Me  (Show Source):
You can put this solution on YOUR website!
.
1.  Read the condition attentively.



2.  You have two rectangles.

    1st rectangle is 30x20 inches.  Its area is 30*20 square inches.

    2nd rectangle has dimensions  (30-x)*(20-x) inches, where "x" is the amount she decreased the dimensions.



3.  The difference of the areas is  30*20 - (30-x)*(20-x) square inches.

    It is the new area to paint it.

    Now your equation is  30*20 - (30-x)*(20-x) = 225.

    Simplify and solve it to find "x".


Answer by math_helper(2461) About Me  (Show Source):
You can put this solution on YOUR website!
a) Original area is +30in+%2A+20in+=+600in%5E2+
Reduce each side by x:
New area is +%2830-x%29%2820-x%29+=+600+-+50x+%2B+x%5E2+
Since we haven't found a value for x yet, that is as far as the new area can be taken (after solving part (b), you can take the value and plug it in to the equation above to get the new area as a numerical value).
b) Assuming the homeowner wants to reduce the area enough to use exactly all 225 sq in of paint:
orig area - new area = 225:
++600+-+%28600+-+50x+%2B+x%5E2%29+=+225+
++50x+-+x%5E2+=+225+
++-x%5E2+%2B+50x+-+225+=+0+
++x%5E2+-+50x+%2B+225+=+0+
++%28x-45%29%28x-5%29+=+0+
x = 45 and/or x = 5
Discard x=45 because the original sides are 20 and 30 and 45 is greater than at least one of these so it doesn't make sense.
x = 5 —> reduce each dimension by +highlight%285in%29+
Back to part (a):
The new area = +600-50%285%29%2B%285%29%5E2+=+highlight%28375in%5E2%29+
=========
Check:
The new dimensions are (20-5) by (30-5) or 15in by 25in:
New area = +15in%2A25in+=+375in%5E2+ (ok)