Write each phrase as a mathematical expression, using x as the variable.
19.One-third of a number, subtracted from 9
20.The product of 4 and a number, divided by 9 more than the number
Solve each problem.
21.The length of a rectangle is 3 m less than twice the width. The perimeter of the rectangle
is 42 m. Find the length and width of the rectangle.
22.In a triangle with two sides of equal length, the third side measures 15 in. less than the sum of
the two equal sides. The perimeter of the triangle is 53 in. Find the lengths of the three sides.
23.A candy clerk has three times as many kilograms of chocolate creams as peanut clusters.
The clerk has 48 kg of the two candies altogether. How many kilograms of peanut clusters
does the clerk have?
24.How many liters of a 20% solution of a chemical should be mixed with 15 L of a
50% solution to get a 30% mixture?
128 CHAPTER 2 Linear Equations, Inequalities, and Applications
Liters Percent Liters of
of Solution (as a decimal) Pure Acid
0.40
x
0.30
2 5.How much water should be added to 30 L
of a 40% acid solution to reduce it to a
30% solution?
2 6.Eric Gorenstein invested some money at
6% and $4000 less than that amount at
4%. Find the amount invested at each
rate if his total annual interest income is
$840.
Rate
Principal (as a decimal) Interest
x 0.06
0.04
2.4
27.A grocery store clerk has $3.50 in dimes and quarters in her cash drawer. The number of
dimes is 1 less than twice the number of quarters. How many of each denomination are
there?
28.When Jim emptied his pockets one evening, he found he had 19 nickels and dimes with a
total value of $1.55. How many of each denomination did he have?
29.Concept Check Which choice is the best estimatefor the average rate for a trip of
405 mi that lasted 8.2 hr?
A.50 mph B.30 mph C.60 mph D.40 mph
- (a)A driver averaged 53 mph and took 10 hr to travel from Memphis to Chicago. What is
the distance between Memphis and Chicago?
(b)A small plane traveled from Warsaw to Rome, averaging 164 mph. The trip took 2 hr.
What is the distance from Warsaw to Rome?
31.A passenger train and a freight train leave
a town at the same time and go in oppo-
site directions. They travel at rates of
60 mph and 75 mph, respectively. How
long will it take for them to be 297 mi
apart?
32.Two cars leave small towns 230 km apart
at the same time, traveling directly to-
ward one another. One car travels 15 km
per hr slower than the other car. They
pass one another 2 hr later. What are
their rates?
Rate Time Distance
Passenger Train 60 x
Freight Train 75 x
Rate Time Distance
Faster car x2
Slower car x- 15 2