Question

@Yuii
Karim is ordering custom T-shirts for his soccer team. Long-sleeved shirts cost $15 each and short-sleeved shirts cost $10 each. Karim can spend at most $250 and he wants to order at least 20 shirts. Let x represent the number of long-sleeved shirts. Let y represent the number of short-sleeved shirts. Select all inequalities that represent constraints for this situation. http://prntscr.com/de9asf
@Yuii

Answer 1

Look, sister!
We need to use what we have to get what we need...

- Long-sleeved shirts cost \(\color{red}{$15}\)
- \(\color{red}x\) represent the number of long-sleeved shirts
>>\(Long-sleeved ~shirts~total~ cost\) = \(\color{blue}{15x}\)

- Short-sleeved shirts cost \(\color{red}{$10}\)
- \(\color{red}y\) represent the number of short-sleeved shirts
>>\(Short-sleeved ~shirts~total~ cost\) = \(\color{blue}{10y}\)

- He wants to order \(\color{red}{at~ least~(\ge)~20}\) shirts
>>\(total ~number ~of~ shirts~TOGETHER~ would ~\color{red}{equal ~to ~20} ~shirts~\color{red}{ or~ more}\)
i.e: \(\color{blue}{x+y\ge20}\)

- Karim can spend \(\color{red}{at ~most ~(\le)~ $250 }\)
>>\(sum ~of ~total~ costs~of~shirts~ should ~NOT ~exceed~ \color{red}{$250}\)
i.e: \(\color{blue}{15x+10y\le250}\)

I think it is clear now to find out your two inequalities which are understood from the question above!!!



and this is also the graphical representation of these two inequalities!
https://www.desmos.com/calculator/tozcuxwu5x

** any point in the overlapped shaded region ( and encountered between the positive direction of y and x-axes) satisfies these two inequalities!

I am with you if you faced any difficulties, @Yuii!