A formula is a “recipe” for performing a certain
calculation. Formulas are often expressed as equations. When we replace the
variable(s) in a formula with numbers and calculate the result, we are
evaluating the formula.
Problem 1
Storm Distance. A formula that has to do with weather is
, where M is your distance in miles from the
storm and t is the time it takes the sound of thunder to reach you. Suppose that
it takes the sound of thunder 14 seconds to reach you. How far is the storm?
Problem 2
Socks from Cotton. Consider the formula 
,
where S is the number of socks of normal size that can be produced from x bales
of cotton. Find the number of socks that can be made from 65 bales.
Problem 3
Distance, Rate, and Time. The distance d that a car will travel at a rate, or
speed, r in time t is given by 
A car travels
at 55 mph for 6.2 hours. How far will it travel?
SOLVING FORMULAS
| Problem 4 |
Problem 5 |
Solve for 
|
Solve for 
|
| Problem 6 |
Problem 7 |
Solve for 
|
Solve for 
|
| Problem 8 |
Problem 9 |
Solve for 
|
Solve for 
|
| Problem 10 |
Problem 11 |
Solve for 
|
Solve for 
|
| Problem 12 |
Problem 13 |
Solve for 
|
Solve for 
|
Section 10.6 – Applications and Problem Solving
FIVE STEPS FOR SOLVING PROBLEMS
Problem 1
Running. In 1997, Yiannis Kouros of Australia set the record for the greatest
distance run in 24 hours by running 188 miles. After 8 hours, he was
approximately twice as far from the finish line as he was from the start. How
far had he run?
Problem 2
Gourmet Sandwiches. A gourmet sandwich shop located near a college campus
specializes in sandwiches prepared in buns of length 18 inches. Suppose Jenny,
Emma, and Sarah buy one of these sandwiches and take it back to their apartment.
Since they have different appetites, Jenny cuts the sandwich in such a way that
Emma gets half of what Jenny gets and Sarah gets three fourth of what Jenny
gets. Find the length of each person’s sandwich.
Problem 3
Interstate Mile Markers. The sum of two consecutive mile markers on I-90 in
upstate New York is 627. Find the numbers on the markers.
Problem 4
Copy Machine Rental. It costs $225 per month plus 1.2 cents per copy to rent a
copy machine. A law firm needs to lease a copy machine for use during a special
case that they anticipate will take 3 months. If they allot a budget of $1400,
how many copies can they make?
Problem 5
Perimeter of High School Basketball Court. The perimeter of a standard high
school basketball court is 268 feet. The length is 34 feet longer than the
width. Find the dimensions of the court.
Problem 6
Average Test Scores. Sam’s average score on his first three math tests is 77. He
scored 62 on the first test. On the third test, he scored 9 more than he scored
on this second test. What did he score on the second and third tests?
Problem 7
Simple Interest . An investment is made at 7% simple interest for one year. It
grows to $8988. How much was originally invested?
Problem 8
Price Before Sale. The price of a suit was decreased to a sale price of $526.40.
This was a 20% reduction . What was the former price?
Problem 9
Boarding Stable. A rancher needs to form a triangular horse pen using ropes next
to a stable. The second angle is three times the first angle. The third angle is
less than the first angle. Find the
angles of the triangular pen.
