1.6b 1.6b ModelingModelingPracticePractice

Right in with practice problems…

When a number is added to its double and its triple, the sum is714. Find the three numbers.

Three numbers: 119, 238, 357Three numbers: 119, 238, 357

2 3 714x x x 6 714x

119x

Guided PracticeThe consumer price index for food and beverages in 1997 was161.3 after a modest 1.7% increase from the previous year.What was the index the previous year?

CPI was approx. 158.6CPI was approx. 158.6

1.017 161.3x 158.604x

Guided PracticeOn their 560-mile trip, a basketball team spent two more hourson the interstate highway than they did on local highways.They average 45 mph on local highways and 55 mph on theinterstate highways. How many hours did they spend drivingon local highways?

t = hours spent on local highways

Distance on local highways: 45tDistance on interstate highways: 55 2t

Guided PracticeOn their 560-mile trip, a basketball team spent two more hourson the interstate highway than they did on local highways.They average 45 mph on local highways and 55 mph on theinterstate highways. How many hours did they spend drivingon local highways?

tt = 4.5 hours = 4.5 hours

t = hours spent on local highways

Total distance travelled: 45 55 2 560t t 45 55 110 560t t

100 450t

Guided PracticeRuth is weighing two job offers from the sales departments oftwo competing companies. One offers a base salary of$25,000 plus 5% of gross sales; the other offers a base salaryof $20,000 plus 7% of gross sales. What would Ruth’s grosssales total need to be to make the second job offer moreattractive than the first? Let x be the gross sales

For the second job to be more attractive than the first, we need:

20,000 0.07 25,000 0.05x x 0.02 5000x

Guided PracticeRuth is weighing two job offers from the sales departments oftwo competing companies. One offers a base salary of$25,000 plus 5% of gross sales; the other offers a base salaryof $20,000 plus 7% of gross sales. What would Ruth’s grosssales total need to be to make the second job offer moreattractive than the first? Let x be the gross sales

For the second job to be more attractive than the first, we need:

250,000x Gross sales would have to exceed $250,000Gross sales would have to exceed $250,000

Guided PracticeFrom 1996 to 1997, the U.S. shipments of personal computersgrew from 26,650,000 to 30,989,000. What was the percentageincrease in U.S. personal computer shipments?

An approximate 16.281% increaseAn approximate 16.281% increase

26,650,000 1 30,989,000x 30,989,000

126,650,000

x

0.16281x

Guided PracticeA chemistry lab keeps two acid solutions on hand. One is 20%acid and the other is 35% acid. How much 20% acid solutionand how much 35% acid solution should be used to prepare25 liters of a 26% acid solution?

x = amount of 20% solution, y = amount of 35% solution

25x y 0.20 0.35 0.26 25x y

25y x

0.20 0.35 25 6.5x x

Guided PracticeA chemistry lab keeps two acid solutions on hand. One is 20%acid and the other is 35% acid. How much 20% acid solutionand how much 35% acid solution should be used to prepare25 liters of a 26% acid solution?

x = amount of 20% solution, y = amount of 35% solution

0.20 0.35 25 6.5x x

0.20 8.75 0.35 6.5x x 15x

xx = 15 liters, = 15 liters, yy = 10 liters = 10 liters