Aaliyah went into a grocery store and bought 5 peaches and 6 mangos, costing a total of $17.75. Tristan went into the same grocery store and bought 2 peaches and 3 mangos, costing a total of $8. Write a system of equations that could be used to determine the price of each peach and the price of each mango. Define the variables that you use to write the system.

Question

Aaliyah went into a grocery store and bought 5 peaches and 6 mangos, costing a total of $17.75. Tristan went into the same grocery store and bought 2 peaches and 3 mangos, costing a total of $8. Write a system of equations that could be used to determine the price of each peach and the price of each mango. Define the variables that you use to write the system.
Answer
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System of Equations:

GPT-4o mini · Answer

Let $ p $ represent the price of each peach, and let $ m $ represent the price of each mango. From the information given, we can formulate the following equations based on Aaliyah's and Tristan's purchases: 1. For Aaliyah's purchase of 5 peaches and 6 mangos costing $17.75: $$ 5p + 6m = 17.75 $$ 2. For Tristan's purchase of 2 peaches and 3 mangos costing $8: $$ 2p + 3m = 8 $$ Thus, the system of equations is: $$ \begin{cases} 5p + 6m = 17.75 \ 2p + 3m = 8 \end{cases} $$ Where: - $ p $ is the price of each peach. - $ m $ is the price of each mango.