Allison went to the grocery store and bought bottles of soda and bottles of juice. Each bottle of soda has 45 grams of sugar and each bottle of juice has 20 grams of sugar. Allison purchased a total of 11 bottles of juice and soda which collectively contain 445 grams of sugar. Write a system of equations that could be used to determine the number of bottles of soda purchased and the number of bottles of juice purchased. Define the variables that you use to write the system

Let's define the variables:

- Let **s** represent the number of bottles of soda that Allison purchased.
- Let **j** represent the number of bottles of juice that Allison purchased.

### Step 1: Total Number of Bottles
We know that Allison purchased a total of 11 bottles of soda and juice. This gives us the equation:

\[
s + j = 11
\]

### Step 2: Total Amount of Sugar
Each bottle of soda has 45 grams of sugar, and each bottle of juice has 20 grams of sugar. Collectively, the bottles contain 445 grams of sugar. This gives us the equation:

\[
45s + 20j = 445
\]

### System of Equations:
\[
\begin{aligned}
1) & \ s + j = 11 \\
2) & \ 45s + 20j = 445
\end{aligned}
\]

This system of equations can be used to determine the number of bottles of soda (**s**) and the number of bottles of juice (**j**) that Allison purchased.

Would you like to solve this system, or need further details?

Here are 5 related questions:
1. How many bottles of soda did Allison purchase?
2. How many bottles of juice did Allison purchase?
3. What is the total weight of sugar if Allison buys 5 bottles of soda and 6 bottles of juice?
4. What happens if each bottle of juice had 30 grams of sugar instead of 20 grams?
5. How much sugar would there be in total if Allison bought only juice?

**Tip:** You can solve systems of equations using either substitution or elimination methods.

Allison went to the grocery store and bought bottles of soda and bottles of juice. Each bottle of soda has 45 grams of sugar and each bottle of juice has 20 grams of sugar. Allison purchased a total of 11 bottles of juice and soda which collectively contain 445 grams of sugar. Write a system of equations that could be used to determine the number of bottles of soda purchased and the number of bottles of juice purchased. Define the variables that you use to write the system.

Solve the system of equations to find out how many bottles of soda and juice Allison purchased. This algebra problem involves creating a system of linear equations from a word problem about total sugar content and bottle quantities. Suitable for students in Grades 6-8.

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