1.6b
Modeling
Practice
Right in with practice
problems…
When a number is added to its double and its triple, the sum is
714. Find the three numbers.
x  2x  3x  714
6x  714
x  119
Three numbers: 119, 238, 357
Guided Practice
The consumer price index for food and beverages in 1997 was
161.3 after a modest 1.7% increase from the previous year.
What was the index the previous year?
1.017 x  161.3
x  158.604
CPI was approx. 158.6
Guided Practice
On their 560-mile trip, a basketball team spent two more hours
on the interstate highway than they did on local highways.
They average 45 mph on local highways and 55 mph on the
interstate highways. How many hours did they spend driving
on local highways?
t = hours spent on local highways
Distance on local highways:
45t
Distance on interstate highways: 55
 t  2
Guided Practice
On their 560-mile trip, a basketball team spent two more hours
on the interstate highway than they did on local highways.
They average 45 mph on local highways and 55 mph on the
interstate highways. How many hours did they spend driving
on local highways?
t = hours spent on local highways
45t  55  t  2  560
45t  55t 110  560
100t  450
t = 4.5 hours
Total distance travelled:
Guided Practice
Ruth is weighing two job offers from the sales departments of
two competing companies. One offers a base salary of
$25,000 plus 5% of gross sales; the other offers a base salary
of $20,000 plus 7% of gross sales. What would Ruth’s gross
sales total need to be to make the second job offer more
attractive 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 x  25, 000  0.05 x
0.02x  5000
Guided Practice
Ruth is weighing two job offers from the sales departments of
two competing companies. One offers a base salary of
$25,000 plus 5% of gross sales; the other offers a base salary
of $20,000 plus 7% of gross sales. What would Ruth’s gross
sales total need to be to make the second job offer more
attractive than the first? Let x be the gross sales
For the second job to be more attractive than the first, we need:
x  250, 000
Gross sales would have to exceed $250,000
Guided Practice
From 1996 to 1997, the U.S. shipments of personal computers
grew from 26,650,000 to 30,989,000. What was the percentage
increase in U.S. personal computer shipments?
26,650,000 1  x   30,989,000
30,989, 000
x
1
26, 650, 000
x  0.16281
An approximate 16.281% increase
Guided Practice
A chemistry lab keeps two acid solutions on hand. One is 20%
acid and the other is 35% acid. How much 20% acid solution
and how much 35% acid solution should be used to prepare
25 liters of a 26% acid solution?
x = amount of 20% solution, y = amount of 35% solution
x  y  25  y  25  x
0.20 x  0.35 y  0.26  25
0.20 x  0.35  25  x   6.5
Guided Practice
A chemistry lab keeps two acid solutions on hand. One is 20%
acid and the other is 35% acid. How much 20% acid solution
and how much 35% acid solution should be used to prepare
25 liters of a 26% acid solution?
x = amount of 20% solution, y = amount of 35% solution
0.20 x  0.35  25  x   6.5
0.20x  8.75  0.35x  6.5  x  15
x = 15 liters, y = 10 liters