Answer:
![4r + 5(20-r) \le 92](https://img.qammunity.org/2021/formulas/mathematics/middle-school/v8ot3gpdsabzebtewpjibu6ppbmnk3acb9.png)
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Step-by-step 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](https://img.qammunity.org/2021/formulas/mathematics/middle-school/v8ot3gpdsabzebtewpjibu6ppbmnk3acb9.png)
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Extra info:
If you want to solve for r, then
![4r + 5(20-r) \le 92](https://img.qammunity.org/2021/formulas/mathematics/middle-school/v8ot3gpdsabzebtewpjibu6ppbmnk3acb9.png)
distribute
![100 - r \le 92](https://img.qammunity.org/2021/formulas/mathematics/middle-school/kpa5heslom9rhsyl95rvvkzvunwominf28.png)
add r to both sides
![100 \le 92+r](https://img.qammunity.org/2021/formulas/mathematics/middle-school/gob01xc289tyxr5u2lmpubro2808cgxt6b.png)
subtract 92 from both sides
![8 \le r](https://img.qammunity.org/2021/formulas/mathematics/middle-school/qxqw1832w1eyyo4wbyw2aql7z7qy2krr5u.png)
![r \ge 8](https://img.qammunity.org/2021/formulas/mathematics/middle-school/hisgr35a6czclnt2c0js8bvgdctsx1qy65.png)
So John must buy at least 8 red pens. The most he can buy is 20 red pens since he wants 20 pens total.