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Wahab wants to donate at least
$6000 in books and pairs of shoes.
Let
B represent the number of books and
S represent the number of pairs of shoes that Wahab must donate to achieve his goal.

20 B+50 S >= 6000
Wahab donates 100 pairs of shoes. What is the least number of books he should donate to achieve his goal?
Choose 1 answer:
(A) Wahab should donate at least 20 books.
(B) Wahab should donate at least 50 books.
(c) Wahab should donate at least 80 books.
(D) Wahab should donate at least 100 books.

Wahab wants to donate at least $\$6000$ in books and pairs of shoes. $\newline$ Let $B$ represent the number of books and $S$ represent the number of pairs of shoes that Wahab must donate to achieve his goal. $\newline$ $20B + 50S \geq 6000$ $\newline$ Wahab donates $100$ pairs of shoes. What is the least number of books he should donate to achieve his goal? $\newline$ Choose $1$ answer: $\newline$ (A) Wahab should donate at least $20$ books. $\newline$ (B) Wahab should donate at least $50$ books. $\newline$ (C) Wahab should donate at least $80$ books. $\newline$ (D) Wahab should donate at least $100$ books.

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Modeling with linear inequalities

Full solution

Q. Wahab wants to donate at least

\$6000

in books and pairs of shoes.

\newline

Let

B

represent the number of books and

S

represent the number of pairs of shoes that Wahab must donate to achieve his goal.

\newline

20B + 50S \geq 6000

\newline

Wahab donates

100

pairs of shoes. What is the least number of books he should donate to achieve his goal?

\newline

Choose

1

answer:

\newline

(A) Wahab should donate at least

20

books.

\newline

(B) Wahab should donate at least

50

books.

\newline

(C) Wahab should donate at least

80

books.

\newline

(D) Wahab should donate at least

100

books.

Understand the problem: Understand the problem. $\newline$ Wahab wants to donate at least $\$6000$ in books and pairs of shoes. The cost of books is represented by $B$ and the cost of pairs of shoes by $S$ . The equation given is $20B + 50S \geq 6000$ . Wahab donates $100$ pairs of shoes, and we need to find the least number of books he should donate to meet his goal.
Substitute known value: Substitute the known value of $S$ into the inequality. Wahab donates $100$ pairs of shoes, so $S = 100$ . Substitute $S$ with $100$ in the inequality $20B + 50S \geq 6000$ . $20B + 50(100) \geq 6000$
Perform multiplication: Perform the multiplication to simplify the inequality. $\newline$ $20B + 50 \times 100 \geq 6000$ $\newline$ $20B + 5000 \geq 6000$
Isolate variable B: Isolate the variable B on one side of the inequality. $\newline$ Subtract $5000$ from both sides of the inequality to solve for B. $\newline$ $20B + 5000 - 5000 \geq 6000 - 5000$ $\newline$ $20B \geq 1000$
Divide sides for B: Divide both sides of the inequality by $20$ to solve for $B$ . $\newline$ $\frac{20B}{20} \geq \frac{1000}{20}$ $\newline$ $B \geq 50$

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