Mathematics
Precalculus. I am not that good at it

Question Description

I’m trying to learn for my Calculus class and I’m stuck. Can you help?

  • Write a problem for a classmate to solve that can be translated to a system of two (2) or more equations in at least two (2) variables. Explain your answer.

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Final Answer

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Problem:

The sum of two numbers is 60, and their product is 675.

Find the two numbers.


Solution:

Let the two numbers be x and y.

Their sum is 60, therefore

x + y = 60          (1)

Their product is 675, therefore

xy = 675            (2)


From (1), obtain

y = 60 - x           (3)

Substitute (3) into (2).

x(60-x) = 675

60x - x^2 = 675

x^2 - 60x + 675 = 0


Factorize to obtain (or you may use the quadratic formula)

(x - 15)(x - 45) = 0

x= 15, or x = 45


When x=15, use (3) to obtain y = 60 - 15 = 45

When x = 45, use (3) to obtain y = 60 - 45 = 15


Answer:

The two numbers are 15 and 45.

Please let me know if you need any clarification. I'm always happy to answer your questions.

abotsi55 (1152)
UT Austin

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