Question

a publishing company prints newspapers and magazines.
let ( n ) represent the number of newspapers and ( m ) represent the number of magazines the company can print with its daily supply of ink cartridges: ( 0.5n + 2.5m leq 6000 )
the company wants to print 8000 newspapers daily. how many magazines at most can the company print daily with the remaining number of ink cartridges?
choose 1 answer:
a the company can print 800 magazines at most.
b the company can print 2500 magazines at most.
c the company can print 6000 magazines at most.
d the company can print 8000 magazines at most.

Explanation:

Step1: Substitute \( N = 8000 \) into the inequality

We have the inequality \( 0.5N + 2.5M \leq 6000 \). Substitute \( N = 8000 \) (since the company wants to print 8000 newspapers) into it:

$$ 0.5\times8000 + 2.5M \leq 6000 $$

Step2: Simplify the left - hand side

Calculate \( 0.5\times8000=4000 \). So the inequality becomes:

$$ 4000 + 2.5M \leq 6000 $$

Step3: Solve for \( M \)

Subtract 4000 from both sides of the inequality:

$$ 2.5M \leq 6000 - 4000 $$

$$ 2.5M \leq 2000 $$

Then divide both sides by 2.5:

$$ M \leq \frac{2000}{2.5} $$

$$ M \leq 800 $$

Answer:

A. The company can print 800 magazines at most.