Question

a hot air balloon can hold up to 300 pounds of weight. the balloons pilot weighs 140 pounds. how many 20 - pound bags of sand (b) can also be carried by the hot air balloon? select three options. -2 0 5 8 10

Explanation:

Step1: Set up the inequality

Let \( b \) be the number of 20 - pound bags of sand. The total weight carried by the balloon is the weight of the pilot plus the weight of the sand bags. So we have the inequality \( 140 + 20b\leqslant300 \).

Step2: Solve the inequality for \( b \)

Subtract 140 from both sides: \( 20b\leqslant300 - 140 \)
\( 20b\leqslant160 \)
Divide both sides by 20: \( b\leqslant\frac{160}{20} \)
\( b\leqslant8 \)

Also, since the number of bags \( b \) cannot be negative (you can't have a negative number of bags), \( b\geqslant0 \). So \( 0\leqslant b\leqslant8 \).

Now we check the options:

• For \( b=- 2 \): It is negative, so it does not satisfy \( b\geqslant0 \).
• For \( b = 0 \): \( 0\) is in the range \( 0\leqslant b\leqslant8 \), so it is valid.
• For \( b = 5 \): \( 5\) is in the range \( 0\leqslant b\leqslant8 \), so it is valid.
• For \( b = 8 \): \( 8\) is in the range \( 0\leqslant b\leqslant8 \) (since \( b\leqslant8 \) and \( 8\geqslant0 \)), so it is valid.
• For \( b = 10 \): \( 10>8 \), so it does not satisfy \( b\leqslant8 \).

Answer:

B. 0, C. 5, D. 8