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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.

Respuesta :

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.

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

Two possible solutions are (a) [tex]3[/tex] pairs of shorts and [tex]5[/tex] t-shirts

                                             (b) [tex]4[/tex] pairs of shorts and [tex]3[/tex] t-shirts.

[tex]x=the\; number\; of shorts\\y=the\; number\; of\ t-shirt\; bought[/tex]

So equation formed is

[tex]16x+10y\leq 100[/tex]

[tex]10y\leq 100-16x\\y\leq 10-1.6x[/tex]---Eq [tex]1[/tex]

Bradon wants at least [tex]2[/tex]  pair of shorts.Therefore

[tex]x\geq 2[/tex]--Eq [tex]2[/tex]

Now put,

[tex]x=3 \\y=10-1.6(3)\\y=10-4.8\\y=5\\[/tex]

Hence [tex]3[/tex] shorts and [tex]5[/tex] t-shirts

Now put,

[tex]x=4 \\y=10-1.6(4)\\y=10-6.4\\y=3\\[/tex]

Now graph the equation,

Learn more about inequalities here:

https://brainly.com/question/15137133?referrer=searchResults

Ver imagen shubheetutor

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