Question

Astrid wants to buy pumpkins and watermelons. She wants to buy more than 10 fruits, and she has a
budget of $117.
P +W > 10 represents the number of pumpkins P and watermelons W Astrid should buy to get more
than 10 fruits.
5.5P +3.5W < 117 represents the number of pumpkins and watermelons she can buy on her budget of
$117.
Does Astrid meet both of her expectations by buying 7 pumpkins and 3 watermelons?

Answer 1

Answer:

Buying 7 pumpkins and 3 watermelons, Astrid doesn't meet her two expectations.

Step-by-step explanation:

Let

P ----> the number of pumpkins and watermelons she can buy

W ----> the number of  watermelons she can buy

we know that

$P+W > 10$ ----> inequality A

$5.5P+3.5W < 117$ ---> inequality B

Note Both inequalities are given in the problem

If Astrid buy 7 pumpkins and 3 watermelons

then

we have the ordered pair (7,3)

Remember that

If a ordered pair is a solution of the system of inequalities, then the ordered pair must satisfy both inequalities

For P=7, W=3

Verify Inequality A

$P+W > 10$

substitute the value of P and the value of W

$7+3 > 10$

$10 > 10$ ----> is not true

so

The ordered pair not satisfy the inequality A

Verify Inequality B

$5.5P+3.5W < 117$

substitute the value of P and the value of W

$5.5(7)+3.5(3) < 117$

$49 < 117$ ----> is true

so

The ordered satisfy the inequality B

therefore

Buying 7 pumpkins and 3 watermelons, Astrid doesn't meet her two expectations.

Answer 2

Answer:

Astrid stays within her budget, but she doesn't buy the expected number of fruits.

Step-by-step explanation:

I just did it on Khan