A full tank contains 8.90

Question

ft.3
of helium, enough to fill 30
balloons.

To calculate the amount of helium needed to fill 50
balloons, first determine the unit rate, which can be calculated as 308.90.
Next, create an equation to represent the relationship between h,
the volume of helium, and b,
the number of balloons: _[blank 1]_. Finally, plug in 50
for b
and solve. The amount of helium needed is _[blank 2]_.

Select two answers: one for blank 1 and one for blank 2.

Responses

blank 2: 18.73
ft.3
blank 2: 18 point 7 3

blank 1: b=308.90h
blank 1: b is equal to 30 over 8 point 9 0 h

blank 2: 168.54
ft.3
blank 2: 168 point 5 4

blank 1: bh=8.9030
blank 1: b over h is equal to 8 point 9 0 over 30

blank 2: 14.83
ft.3
blank 2: 14 point 8 3

blank 1: b=8.9030h

Answer 1

To fill in the blanks correctly:

• For blank 1, the equation that represents the relationship between \( h \), the volume of helium, and \( b \), the number of balloons can be derived from the given information. You can calculate the volume of helium per balloon and set up the equation as follows:

Let \( h = \) volume of helium needed (in ft³) and \( b = \) number of balloons.

Since 8.90 ft³ fills 30 balloons, the unit rate is: \[ \frac{8.90 , \text{ft}^3}{30 , \text{balloons}} = \frac{h}{b} \] Thus the equation can be rewritten as: \[ b = \frac{8.90}{30}h \] However, if we want to express the relationship in the terms of \( h \) it will lead to: \[ h = \frac{30}{8.90}b \]

So for blank 1, the correct response is:

• blank 1: \( h = \frac{8.90}{30}b \).

Next, to calculate how much helium is needed for 50 balloons:

Using the formula derived above, we substitute \( b = 50 \): \[ h = \frac{8.90}{30} \times 50 \] Calculating that gives: \[ h = 14.83 , \text{ft}^3 \]

Therefore, for blank 2, the correct response is:

• blank 2: 14.83 ft.³.

So, the two answers are:

• blank 1: \( h = \frac{8.90}{30}b \)
• blank 2: 14.83 ft.³