Question 233551
Jerry is a purchasing agent for his company,and has a budget of $750,000 to purchase 600 new computers for the company staff. He has narrowed his choices to two different brands: Lateway, with a cost of 1,200 per computer, and cracintosh, with a cost of $1,450 each. In order to spend the budgeted amount exactly, how many employees will each receive a Cranintosh computer?
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Value + value = value
1200x + 1450(600-x) = 750,000
1200x + 1450*600 - 1450x = 750,000
-250x = -120000
x = 480 (# of employees will receive a Lateway)
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600-x = 120 (# of employees will receive a Cranintosh)
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second problem 
Jerry and his girlfriend Gerri live 326 miles apart. One day, Jerry decides to surprise Geri by driving to her place unannounced. He leaves at 10:00 a.m. and drives at an average speed of 68 m.p.h. Of course, it just so happens that Gerri had the same idea, and she left her place to surprise Jerry at 9:30 a.m., driving at an average speed of 76 m.p.h. At what time do they pass each other on the road? How far are they from Jerrys' place at that momement?
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J to G DATA:
rate = 68 mph ; time = x hrs ; distance = 68x miles
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G to J DATA:
rate = 76 mph ; time = (x+1/2) hrs ; distance = 76(x+(1/2)) miles
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Equation:
distance + distance = 326 miles
68x + 76(x+(1/2)) = 326
68x + 76x + 38 = 326
144x = 288
x = 2 hrs (They pass each other after Jerry has driven 2 hrs; at 12:00
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At that time Jerry is 2*68 = 136 miles from his starting point.
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third problem 
Jerry will soon attend a sold-out concert at a local amphitheater. There are two types of seating available: reserved seating close to the stage and general admission seating on the lawn. Reserved tickets are $34 and lawn tickets are $20. the total seating in the amphitheater is 16,000. If the total gate receipts (profit from ticket sales) are $409,600 how many folks will join Jerry on the lawn?
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Equation:
Quantity Eq::R + L = 16000
Value Eq::::34R + 20L = 409,600
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Multiply through the Quantity Eq. by 34 to get:
34R + 34L = 34*16000
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Subtract that from the Value Eq to get:
-14L = -134400
Divide to solve for L:
L = 9600 (# that will join Jerry on the lawn)
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Cheers,
Stan H.