Expert: Socrates - 7/31/2006

Question
I am having a lot of troble in writing a system of inequalities such as this, if you have $2,000 to invest in 2 investments, telecommunications and pharmaceuticals. The telecommunications investment is to be no more than 4 times the pharmaceutical investment. I have 4x = my amount invested in telecommunications and y = my investment in pharmaceuticals. In writing a system of inequalities for this problem would x + y = $ 2,000 and how would you write the intire system of inequalities with a step by step explanation.

Answer
Let
t = the amount in telecomunications
p = the amount invested in pharmaceuticals

the total amount invested is $2000

so t + p = 2000

The telecommunications investment is to be no more than 4 times the pharmaceutical investment.

This means that t <= 4p (the most t can be is 4p)

So the entire system is

t + p = 2000
t <= 4p

Of course, if you prefer, you can change t and p to x and y