Question

A store sells black ink pens for $5 and red ink pens for $4. John wishes to buy 20 pens but doesn’t wish to spend more than $92. Writing r for the number of red pens, form an inequality to show this information

Answer 1

Answer:  $4r + 5(20-r) \le 92$

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Explanation:

r = number of red pens

4r = cost of buying r red pens

example: if r = 10, then 4r = 4*10 = 40 is the total cost of buying 10 red pens

If John buys r red pens, then he must buy 20-r black pens so that r and 20-r add to 20.

John buys 20-r black pens, and at $5 each, so it will cost 5(20-r) dollars for just the black pens alone.

In total, John spends 4r + 5(20-r) dollars for all the pens (red & black)

We want $92 be the most he spends. This is the ceiling or highest value possible.

Therefore,

$4r + 5(20-r) \le 92$

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Extra info:

If you want to solve for r, then

$4r + 5(20-r) \le 92$

$4r + 5(20)+5(-r) \le 92$ distribute

$4r + 100 - 5r \le 92$  

$100 - r \le 92$

$100-r+r \le 92+r$ add r to both sides

$100 \le 92+r$

$100-92 \le 92+r-92$ subtract 92 from both sides

$8 \le r$

$r \ge 8$

So John must buy at least 8 red pens. The most he can buy is 20 red pens since he wants 20 pens total.