Okay. I have some trouble with this word problem Using Quadratic equation. Could someone help please?


1.)The sum of a number and its reciprocal is 26/5. Find the number.

2.)One positive integer is three larger than another positive integer. The sum of the squares of these integers is one less than three times the product of the integers. Find these integers.

3.)A piece of wire 24cm long is cut into two pieces, and each piece is bent to form a square frame. Determine how the wire should be cut to make two squares of minimum total area. What is the minimum total area?

Whenever you do a word problem the first step is to identify the unknown quantities and assign them a letter.

So for your first question, let n = unknown number.

The next step is to read the problem and identify the key words and what they mean mathematically.

In the first question two words are key words:
'sum' which means the answer to an addition problem and
'reciprical' which means 1 divided by the number

The third step is to translate the question into mathematics.

Your first question then becomes:

n + 1/n = 26/5

which when you multiply by the lowest common denominator (5n) becomes
5n^2 + 5 = 26n

Which rearranges into

5n^2 -26n + 5 = 0

You now have a quadratic equation which you can solve to find the answer.

A crew row 7 miles downstream and back in 200 minutes.If the river runs at 2 knots,what is the boat's speed in still water?

Please start your own thread.

Is that 7 miles down and 7 miles back or 7 miles altogether?
The problem can be taken either way.

Regardless, lets assume it is 7 miles down and 7 miles back.

Since we are given the total time as 200 minutes, or 10/3 hours, we can use d/r=t.

Rowing with the stream, the rate is r+2 and the rate upstream is r-2.

\frac{7}{r+2}+\frac{7}{r-2}=\frac{10}{3}

Solve for r. That is the boats speed in still water.