Math 1005 Section 1.3 Models and Applications
Let x represents the number. Use the given conditions to write an equation. Solve the
equation and find the number.
1. When 80% of a number is added to the number, the result is 252. What is the
number?
2. Five more than four times a number is that number increased by 35. Find the number.
3. Growth in human populations and economic activity threatens the continued existence
of salmon in the Pacific Northwest. The data can be modeled by the formula
P = −.22t + 9.6 in which P is the salmon population, in millions, t years after 1960.
When will there be no Pacific salmon? Round to the nearest year.
4. In 2001, the most populous countries in the world were China and India. In that year,
China’s population exceeded India’s by 260 million. Combined, the two countries had a
population of 2310 million. Determine the 2001 population for China and the 2001
population for India.
5. A car rental agency charges $180 per week plus $0.25 per mile to rent a car. How
many miles can you travel in one week for $395?
6. You inherit $18,750 with the stipulation that for the first year the money must be
placed in two investments paying 10% and 12% annual interest, respectively. How
much should be invested at each rate if the total interest earned for the year is to be
$2117?
7. A rectangular soccer field is twice as long as it is wide. If the perimeter of the
soccer field is 300 yards, what are its dimensions?
8. A repair bill on a yacht came to $1063, including $532 for parts and the remainder
for labor. If the cost of labor is $63 per hour, how many hours of labor did it take to
repair the yacht?
9. Including 8% sales tax, an inn charges $162 per night. Find the inn’s nightly cost
before tax is added.