Question

lena is planning a bubble - themed birthday party for her little sister. she buys a jug of bubble solution and divides it equally among 8 small bottles. each small bottle holds 2 ounces of bubble solution. let b represent the amount of bubble solution in the jug to start. which equation models the problem?\\(\frac{b}{8}=2\\)\\(2b = 8\\)solve this equation to find the amount of bubble solution in the jug to start.\\(\square\\) ounces\\(\text{work it out}\\)\\(\text{not feeling ready yet? these can help:}\\)

Explanation:

Part 1: Identifying the Correct Equation

We know that Lena divides the total bubble solution \( b \) into 8 bottles, and each bottle has 2 ounces. So the total amount \( b \) divided by the number of bottles (8) should equal the amount per bottle (2). So the equation is \( \frac{b}{8}=2 \). The other equation \( 2b = 8 \) would imply a different relationship (total is 8 and per bottle is \( \frac{8}{2}=4 \), which is not the case here).

Step 1: Multiply both sides by 8

To isolate \( b \), we multiply both sides of the equation \( \frac{b}{8}=2 \) by 8. This is because the inverse operation of division (by 8) is multiplication (by 8).
\( \frac{b}{8}\times8 = 2\times8 \)

Step 2: Simplify both sides

Simplifying the left side, \( \frac{b}{8}\times8=b \). Simplifying the right side, \( 2\times8 = 16 \). So we get \( b = 16 \).

Answer:

\(\boldsymbol{\frac{b}{8}=2}\)

Part 2: Solving the Equation \( \frac{b}{8}=2 \)