Math ! 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

(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

f

step-by-step explanation:

f

step-by-step explanation: