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Jeanette R.

asked • 03/04/18

PLEASE HELP!!! question: Two positive numbers have the property that one more than the first number plus four less than three times the second, totals to 100.

(i) If we call the first number x, and the second z, write an equation that relates
these numbers.
(ii) Use (i) to write an equation that gives the second in terms of the first.
(iii) Use (ii) to write an expression for y=f (x), the product of these two numbers, in
terms of x.
(iv) Now write the product formula in vertex form, by using the completing the
square technique. (HINT: It will be much easier if you start out multiplying both
sides of (iii) by -3.)
(v) Use (iv) to graph the function in (iii). Label the coordinates of the maximum
product, as well as both x-intercepts.
(vi) Find both numbers, as well as the largest product two numbers can have, under
these conditions.
(vii) Write a complete sentence explanation of the answers to (vi)

Mark M.

In  the problem statement you say the numbers "total" 100.
In iii and iv you ask for the product.
Which is it?


2 Answers By Expert Tutors


Al P. answered • 03/05/18

New to Wyzant

Precalculus tutoring

Al P.

I assumed x and z are nonnegative (zero is neither positive nor negative and I assumed they can be zero).  For nonnegative x and z, the parabola is cut off where it meets the x-axis (and the graph includes the x-axis).  
If they must be strictly positive, then the graph does not include the x-axis and there are no x-intercepts.  


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