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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\$6000 in books and pairs of shoes.\newlineLet BB represent the number of books and SS represent the number of pairs of shoes that Wahab must donate to achieve his goal.\newline20B+50S≥600020B + 50S \geq 6000\newlineWahab donates 100100 pairs of shoes. What is the least number of books he should donate to achieve his goal?\newlineChoose 11 answer:\newline(A) Wahab should donate at least 2020 books.\newline(B) Wahab should donate at least 5050 books.\newline(C) Wahab should donate at least 8080 books.\newline(D) Wahab should donate at least 100100 books.

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Full solution

Q. Wahab wants to donate at least $6000\$6000 in books and pairs of shoes.\newlineLet BB represent the number of books and SS represent the number of pairs of shoes that Wahab must donate to achieve his goal.\newline20B+50S≥600020B + 50S \geq 6000\newlineWahab donates 100100 pairs of shoes. What is the least number of books he should donate to achieve his goal?\newlineChoose 11 answer:\newline(A) Wahab should donate at least 2020 books.\newline(B) Wahab should donate at least 5050 books.\newline(C) Wahab should donate at least 8080 books.\newline(D) Wahab should donate at least 100100 books.
  1. Understand the problem: Understand the problem.\newlineWahab wants to donate at least $6000\$6000 in books and pairs of shoes. The cost of books is represented by BB and the cost of pairs of shoes by SS. The equation given is 20B+50S≥600020B + 50S \geq 6000. Wahab donates 100100 pairs of shoes, and we need to find the least number of books he should donate to meet his goal.
  2. Substitute known value: Substitute the known value of SS into the inequality. Wahab donates 100100 pairs of shoes, so S=100S = 100. Substitute SS with 100100 in the inequality 20B+50S≥600020B + 50S \geq 6000. 20B+50(100)≥600020B + 50(100) \geq 6000
  3. Perform multiplication: Perform the multiplication to simplify the inequality.\newline20B+50×100≥600020B + 50 \times 100 \geq 6000\newline20B+5000≥600020B + 5000 \geq 6000
  4. Isolate variable B: Isolate the variable B on one side of the inequality.\newlineSubtract 50005000 from both sides of the inequality to solve for B.\newline20B+5000−5000≥6000−500020B + 5000 - 5000 \geq 6000 - 5000\newline20B≥100020B \geq 1000
  5. Divide sides for B: Divide both sides of the inequality by 2020 to solve for BB.\newline20B20≥100020\frac{20B}{20} \geq \frac{1000}{20}\newlineB≥50B \geq 50

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