Mrs. Smith decides to buy three sweaters and a pair of jeans. she had $120 in her wallet. if the price of jeans is $35, what is the highest possible price (p) of a sweater, if each sweater, if each sweater is the same price? write, solve, and graph the inequality.

We already know that price [tex]j[/tex] of jeans is $35.Let's say Mrs.Smith buys 3 sweaters for [tex]p[/tex] dollars each, and since her budget is $120 we have the inequality:

[tex]3p+j\leq 120\\ \\\\=3p+35\leq 120[/tex]

Therefore

[tex]p\leq 28.33[/tex]

Thus the maximum price of a sweater is $28.33

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jajumonac jajumonac · Answer 2 · 2020-04-23T03:33:08+02:00

Answer:

The highest price possible of a sweater is $28.33.

Givens

Mrs. Smith decides to by three sweaters and a pair of jeans.
She had $120, that's the restriction, so she cannot spend more than that.

Let's represents sweaters with x and jeans with y. The inequality that models this situation is

[tex]3x+y\leq 120[/tex]

There you can observe the money restriction and the exact number per item she wants to buy.

To find the solution of this inequality, we have to draw the line [tex]3x+y=120[/tex], which represents the border of the solution area.

Then, we evaluate the inequality with a test point (0,0).

The image attached shows the result of this process. Notice that the solution area is below the line, beacuse (0,0) must be part of the solution area.

However, we already know that jeans costs $35, replacing it in the expression, we have

[tex]3x+35\leq 120\\x=\leq \frac{120-35}{3}\\ x\leq 28.33[/tex]

Therefore, the highest price possible of a sweater is $28.33.

(The second image attached shows this result)