SOLUTION: Janice has enough money to purchase pebbles to cover 74 square feet. She wishes to form a border around her pool. The pool measures 25 ft. in length and 10 ft. in width. How wid

Question 139276: Janice has enough money to purchase pebbles to cover 74 square feet. She wishes to form a border around her pool. The pool measures 25 ft. in length and 10 ft. in width. How wide should she make the border?
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
Presuming that she wants to make a uniform border (same width all the way around), let that measurement be x.

Since she will have the width of the border all the way around the pool, the overall dimensions are increased by 2x in each direction -- one width of x on one side, and another width of x on the other side, top and bottom, same thing.

The area of the pool is given by square feet.

The overall area of the pool and the border has to be 250 plus 74 because she can only afford 74 sq feet of pebbles. But the overall area has to be and this is the expression that has to equal 324 square feet.

Expand the binomials:

Collect like terms and put the equation into standard () form.

Divide by 2 to make the coefficients smaller and more manageable:

This ugliness actually factors, believe it or not:

Using the Zero Product Rule:
or . Exclude the extraneous negative root introduced by squaring the variable in the process of solving the problem (we are looking for a positive measure of length, after all) and you can see your answer is 1 foot.

Check:

Answer checks.
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