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A contractor is managing three different job sites. It costs her $c to employ a carpenter, $p to employ a plumber, and $e to employ an electrician. The total cost to employ carpenters, plumbers, and electricians at each site is

Cost at site 1 = 12c+2p+4e.

Cost at site 2= 14c+ 5p+3e.

Cost at site 3= 17c+p+5e.

Write expressions in terms of c, p, and e for:

(a) the total employment cost for all three sites

(b) the difference between the employment cost at site 1 and site 3.

(c) the amount remaining in the contractor's budget after accounting for the employment cost at all three sites, given that originally the budget is 50c+10p+20e.

A contractor is managing three different job sites It costs her c to employ a carpenter p to employ a plumber and e to employ

Answer :

Total cost: 43c + 8p + 12e

Difference between site 1 and 3: -5c + p - e

Amount remaining in budget: 7c + 2p + 8e

a) Total employment cost for all three sites:

Site 1 cost: 12c + 2p + 4e

Site 2 cost: 14c + 5p + 3e

Site 3 cost: 17c + p + 5e

Therefore, the total cost is:

Total cost = Site 1 cost + Site 2 cost + Site 3 cost

= (12c + 2p + 4e) + (14c + 5p + 3e) + (17c + p + 5e)

= 43c + 8p + 12e

b) Difference between employment cost at site 1 and site 3:

Site 1 cost: 12c + 2p + 4e

Site 3 cost: 17c + p + 5e

Difference = Site 1 cost - Site 3 cost

= (12c + 2p + 4e) - (17c + p + 5e)

= -5c + p - e

c) Amount remaining in the budget:

Initial budget: 50c + 10p + 20e

Total cost: 43c + 8p + 12e (from part a)

Amount remaining = Initial budget - Total cost

= (50c + 10p + 20e) - (43c + 8p + 12e)

= 7c + 2p + 8e

Therefore, the expressions for the contractor's employment costs are:

Total cost: 43c + 8p + 12e

Difference between site 1 and 3: -5c + p - e

Amount remaining in budget: 7c + 2p + 8e

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