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Jaden and Lola are hosting events that are catered by the same company. Jaden plans to have 82 adults and 96 children attend, so the total projected cost of his meals is $5,664. Lola has 65 adults and 49 children on his guest list, so she will pay the caterer $4,002. How much does the caterer charge for each meal?

Jaden and Lola are hosting events that are catered by the same company Jaden plans to have 82 adults and 96 children attend so the total projected cost of his m class=

Respuesta :

Let's use the variable x to represent the cost of one adult meal, and y to represent the cost of one child meal.

If the cost of 82 adult meals and 96 children meals is $5,664, we can write the following equation:

[tex]82x+96y=5664[/tex]

If the cost of 65 adult meals and 49 children meals is $4,002, we can write the equation:

[tex]65x+49y=4002[/tex]

To solve this system, let's solve the second equation for y and then use its value in the first equation:

[tex]\begin{gathered} 65x+49y=4002 \\ 49y=4002-65x \\ y=\frac{4002-65x}{49} \\ \\ 82x+96y=5664 \\ 82x+96(\frac{4002-65x}{49})=5664 \\ 82x+7840.653-127.347x=5664 \\ -45.347x=-2176.653 \\ x=48 \\ \\ y=\frac{4002-65\cdot48}{49} \\ y=18 \end{gathered}[/tex]

Therefore every adult meal costs $48 and every child's meal costs $18.