Brandon is shopping at old navy during a sale. all shorts are $16 each and all t-shirts are $10 each. he has $100 to spend and would like to purchase at least 2 pairs of shorts. a) write a system of linear inequalities to represent this situation, then graph. b)using your graph, give two possible combinations of shorts and brandon can buy.

Let
x = the number of shorts bought
y =  the number of t-shirts bought

A pair of shorts costs $16 and a t-shirt costs $10. Brandom has $100 to spend.
Therefore
16x + 10y ≤ 100
This may be written as
y ≤ - 1.6x + 10                 (1)

Brandon wants at least 2 pairs of shorts. Therefore
x ≥ 2                               (2)

Graph the equations y = -1.6x + 10 and  x = 2.
The shaded region satisfies both inequalities.

Two possible solutions are
(a) 3 pairs of shorts and 4 t-shirts,
(b) 4 pairs of shorts and 2 t-shirts.

Two possible solutions are (a) pairs of shorts and t-shirts

                                             (b) pairs of shorts and t-shirts.

So equation formed is

---Eq

Bradon wants at least  pair of shorts.Therefore

--Eq

Now put,

Hence shorts and t-shirts

Now put,

Now graph the equation,

Learn more about inequalities here:

link

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