Question

Carolina goes to a paintball field that charges an entrance fee of \$18$18dollar sign, 18 and \$0.08$0.08dollar sign, 0, point, 08 per ball. The field has a promotion that says, "Get \$10$10dollar sign, 10 off if you spend \$75$75dollar sign, 75 or more!" Carolina wonders how many paintballs she needs to buy along with the entrance fee to get the promotion.
Let BBB represent the number of paintballs that Carolina buys.
1) Which inequality describes this scenario?
Choose 1 answer:
Choose 1 answer:

(Choice A)
A
18+0.08B \leq 7518+0.08B≤7518, plus, 0, point, 08, B, is less than or equal to, 75

(Choice B)
B
18+0.08B \geq 7518+0.08B≥7518, plus, 0, point, 08, B, is greater than or equal to, 75

(Choice C)
C
18+0.08B \leq 1018+0.08B≤1018, plus, 0, point, 08, B, is less than or equal to, 10

(Choice D)
D
18+0.08B \geq 1018+0.08B≥1018, plus, 0, point, 08, B, is greater than or equal to, 10
2) What is the smallest number of paintballs that Carolina can buy along with the entrance fee to get the promotion?
paintballs

Answer 1

Inequalities are used to show unequal expressions; in other words, it is the opposite of equalities.

The inequality that represents the scenario is, $18 + 0.08B \ge 75$ and the smallest number of balls Carolina can buy is 713

Given that:

$Entrance\ Fee = \ 18$

$Rate = \ 0.08$ per ball

Let:

$B \to Balls$

The amount (A) Carolina can spend on B balls is:

A = Entrance Fee + Rate * B

This gives:

$A = 18 + 0.08 * B$

$A = 18 + 0.08B$

To get $10, Carolina must spend $75 or more.

This means:

$A \ge 75$

So, the inequality is:

$18 + 0.08B \ge 75$

The smallest number of balls is calculated as follows:

$18 + 0.08B \ge 75$

Collect like terms

$0.08B \ge 75 - 18$

$0.08B \ge 57$

Divide both sides by 0.08

$B \ge 712.5$

Round up

$B \ge 713$

Hence, the inequality is $18 + 0.08B \ge 75$ and the smallest number of balls is 713

Learn more about inequalities at:

brainly.com/question/20383699

Answer 2

Using a linear function, it is found that:

• 1. $18 + 0.08B \geq 75$, given by option B.
• 2. She has to buy at least 713 paintballs.

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The linear function for the cost of B paintballs has the following format:

$C(B) = C(0) + aB$

In which

• C(0) is the fixed cost.
• a is the cost per paintball.

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Question 1:

• Entrance fee of $18, thus $C(0) = 18$.
• Cost of $0.08 per ball, thus, $a = 0.08$

Thus:

$C(B) = 18 + 0.08B$

• The promotion is valid if the cost is of at least 75, thus:

$C(B) \geq 75$

$18 + 0.08B \geq 75$, given by option B.

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Question 2:

• The smallest number is the solution of the inequality for B, thus:

$18 + 0.08B \geq 75$

$0.08B \geq 57$

$B \geq \frac{57}{0.08}$

$B \geq 712.5$

Rounding up, she has to buy at least 713 paintballs.

A similar problem is given at https://brainly.com/question/24583430