Question

lesson 2 homework period________ use the following information for questions 1-4. an insulin pump can hold 200 ml of insulin per pump. the current price per vial (200 ml) is approximately $145. 1. determine an equivalent ratio to represent the same relationship per dollar. round to the nearest thousandth. $145 \over 1 \text{vial(s)} \approx $1 \over \text{vial(s)} - each vial of insulin will cost you ____ dollars. - if you need to fill 4.5 pumps, how much will you spend?

Explanation:

Part 1: Determine the equivalent ratio per dollar (vials per dollar)

Step 1: Set up the proportion

We know that \(\frac{\$145}{1 \text{ vial}}=\frac{\$1}{x \text{ vials}}\), where \(x\) is the number of vials per dollar. To solve for \(x\), we can cross - multiply: \(145x = 1\times1\).

Step 2: Solve for \(x\)

From \(145x=1\), we get \(x=\frac{1}{145}\). Calculate \(\frac{1}{145}\approx0.00689655\). Rounding to the nearest thousandth, we look at the fourth decimal place. The fourth decimal place is 6, which is greater than or equal to 5, so we round up the third decimal place. So \(x\approx0.007\).

Part 2: Cost of each vial

The cost of each vial is given as \(\$145\) (since 1 vial costs \(\$145\)).

Part 3: Cost to fill 4.5 pumps

Step 1: Determine the number of vials needed

Since each pump holds 200 mL (1 vial) and we need to fill 4.5 pumps, we need 4.5 vials.

Step 2: Calculate the total cost

The cost per vial is \(\$145\), so the total cost \(C = 145\times4.5\). Calculate \(145\times4.5=(100 + 40+5)\times4.5=100\times4.5+40\times4.5 + 5\times4.5=450+180 + 22.5 = 652.5\).

Answer:

s:

• Equivalent ratio per dollar: \(\frac{\$1}{0.007 \text{ vials}}\) (or the number of vials per dollar is approximately \(0.007\))
• Cost of each vial: \(\$145\)
• Cost to fill 4.5 pumps: \(\$652.5\)