Question

jacob went to the grocery store and bought bottles of soda and bottles of juice. each bottle of soda has 25 grams of sugar and each bottle of juice has 10 grams of sugar. jacob purchased a total of 12 bottles of juice and soda which collectively contain 240 grams of sugar. determine the number of bottles of soda purchased and the number of bottles of juice purchased.
answer attempt 1 out of 2
jacob purchased \\(\square\\) bottles of soda and \\(\square\\) bottles of juice.

Explanation:

Step1: Define variables

Let \( x \) be the number of soda bottles and \( y \) be the number of juice bottles. We have two equations:

1. \( x + y = 12 \) (total number of bottles)
2. \( 25x + 10y = 240 \) (total sugar content)

Step2: Solve the first equation for \( y \)

From \( x + y = 12 \), we get \( y = 12 - x \).

Step3: Substitute \( y \) into the second equation

Substitute \( y = 12 - x \) into \( 25x + 10y = 240 \):
\[

$$\begin{align*} 25x + 10(12 - x) &= 240 \\ 25x + 120 - 10x &= 240 \\ 15x + 120 &= 240 \\ 15x &= 240 - 120 \\ 15x &= 120 \\ x &= \frac{120}{15} \\ x &= 8 \end{align*}$$

\]

Step4: Find \( y \)

Substitute \( x = 8 \) into \( y = 12 - x \):
\( y = 12 - 8 = 4 \)

Answer:

Jacob purchased \( \boldsymbol{8} \) bottles of soda and \( \boldsymbol{4} \) bottles of juice.