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Math Help!!!!!!!

1. Betty, Dawnie, and Joan share the same birthday. They’ve decided to join together to have one big birthday party. The event location says it will cost $80 for the rental of the space and $10 per guest. Each girl invites x number of guests, including themselves in their guest count.

The girls have each written a different expression to represent the total cost of the party. Explain how each expression represents the final cost.
(a) Betty’s expression: 10x + 10x + 10x + 80
(b) Dawnie’s expression: 10(x + x + x) + 80
(c) Joan’s expression: x(10 + 10 + 10) + 80

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smmwaite

Answers and Explanation

(a) Betty’s expression:

Cost of guest = 10 × x + 10 × x + 10 × x

                    = 10x + 10x + 10x

cost of the venue = 80

Total cost = 10x + 10x + 10x + 80

(b) Dawnie’s expression:

Cost of the location  = $80

Number of guests = x + x + x

Cost of all guests = $10(x + x + x)

Total cost = 10(x + x + x) + 80

(c) Joan’s expression:

Cost of the location = 80

Cost of guest = 10 × x + 10 × x + 10 × x

                    = 10x + 10x + 10x

                    = x(10 + 10 + 10)     ⇒  After factoring out x.  

Total cost = x(10 + 10 + 10) + 80



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