Youssef is taking a trip on an airplane. He knows that to avoid extra fees his suitcase must weigh under 50 pounds. The suitcase with his clothes weighs 35 pounds. He has room, so he decides to pack some books for his trip, too. Each book weighs on average 1.2 pounds. He writes the inequality 1.2b+35

Question

Youssef is taking a trip on an airplane. He knows that to avoid extra fees his suitcase must weigh under 50 pounds. The suitcase with his clothes weighs 35 pounds. He has room, so he decides to pack some books for his trip, too. Each book weighs on average 1.2 pounds. He writes the inequality 1.2b+35<50 , where  b  equals the number of books, to help figure this out. Solve his inequality. Use the letter  b  as your variable and write your  b  term first. After solving the inequality, use your answer to determine how many whole books Youssef can bring on his trip

GPT-4o mini · Answer

To solve the inequality $1.2b + 35 < 50$, we first isolate the term with $b$. 1. Subtract 35 from both sides: $$ 1.2b < 50 - 35 $$ $$ 1.2b < 15 $$ 2. Next, divide both sides by 1.2: $$ b < \frac{15}{1.2} $$ 3. To simplify $\frac{15}{1.2}$, we can convert 1.2 to a fraction: $$ 1.2 = \frac{12}{10} = \frac{6}{5} $$ 4. Now, we rewrite $\frac{15}{1.2}$ using this fraction: $$ \frac{15}{1.2} = 15 \times \frac{5}{6} = \frac{75}{6} = 12.5 $$ 5. Therefore, the inequality becomes: $$ b < 12.5 $$ Since $b$ must be a whole number, the largest whole number less than 12.5 is 12. Thus, Youssef can bring a maximum of **12 whole books** on his trip.