Question

Jose's banquet hall charges a one time fee of $100 plus $50 per guest for weddings. Another wedding venue, Palace of Aaron, Charges a one-time fee of $200 in addition to $45 per guest. Letting "g" represent the number of wedding guests, Write an algebraic expression to represent the cost of renting each of the banquet halls.

(First part)




(Second part)
At how many wedding guests is the cost the same for both venues? Show your work.​

Answer 1

Part 1:

Jose's Banquet Hall: 50g+100

Palace of Aaron: 45g+200

Part 2:

20 guests

Explanation:

Part 1:

$50 per guest plus $100 fee

50g+100

$45 per guest plus $200 fee

45+200

Part 2:

$50(20)+$100=$1100

$45(20)+$200=$1100

Answer 2

II.
`\displaystyle 20\:wedding\:guests`

I.
`\displaystyle 100 + 50g = 200 + 45g`

Explanation:

100 + 50g = 200 + 45g

- 200 - 50g - 200 - 50g

___________________

`\displaystyle (-100)/(-5) = (-5g)/(-5) \\ \\ 20 = g`

So, at twenty wedding guests, the cost will balance for both venues.

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