Question

1. sam bought 15 bottles of orange juice and grape juice. the bottles of orange juice, o, were on sale for $2 per bottle, and the bottles of grape juice, g, were on sale for $3 per bottle. sam spent a total of $36. how many bottles of orange juice and grape juice did sam buy? this is represented by the following two equations:

o + g = 15
2o + 3g = 36
______ bottles of orange juice
______ bottles of grape juice

Explanation:

Step1: Solve for \( o \) from first equation

From \( o + g = 15 \), we get \( o = 15 - g \).

Step2: Substitute \( o \) into second equation

Substitute \( o = 15 - g \) into \( 2o + 3g = 36 \):
\( 2(15 - g) + 3g = 36 \)
\( 30 - 2g + 3g = 36 \)
\( 30 + g = 36 \)
\( g = 36 - 30 = 6 \).

Step3: Find \( o \) using \( o = 15 - g \)

\( o = 15 - 6 = 9 \).

Answer:

9 bottles of orange juice
6 bottles of grape juice