6.Suppose that you know that two angles of a triangle have equal measures and the third
angle measures 36°. How would you find the measures of the equal angles without actu-
ally writing an equation?
7.In a problem about the number of coins of different denominations, would an answer that
is a fraction be reasonable? Would a negative answer be reasonable?
8.In a motion problem the rate is given as xmph and the time is given as 10 min. What vari-
able expression represents the distance in miles?Solve each problem. See Example 1.
9.Otis Taylor has a box of coins that he uses
when he plays poker with his friends. The
box currently contains 44 coins, consist-
ing of pennies, dimes, and quarters. The
number of pennies is equal to the number
of dimes, and the total value is $4.37.
How many of each denomination of coin
does he have in the box?10.Nana Nantambu found some coins while
looking under her sofa pillows. There
were equal numbers of nickels and quar-
ters and twice as many half-dollars as
quarters. If she found $2.60 in all, how
many of each denomination of coin did
she find?
11.In Canada, $1 and $2 bills have been replaced by
coins. The $1 coins are called “loonies” because
they have a picture of a loon (a well-known Cana-
dian bird) on the reverse, and the $2 coins are called
“toonies.” When Marissa returned home to San
Francisco from a trip to Vancouver, she found that
she had acquired 37 of these coins, with a total
value of 51 Canadian dollars. How many coins of
each denomination did she have?
12.Dan Ulmer works at an ice cream shop. At the end of his shift, he counted the bills in his
cash drawer and found 119 bills with a total value of $347. If all of the bills are $5 bills
and $1 bills, how many of each denomination were in his cash drawer?
13.Dave Bowers collects U.S. gold coins. He has a collection of
41 coins. Some are $10 coins, and the rest are $20 coins. If the
face value of the coins is $540, how many of each denomina-
tion does he have?
14.In the 19th century, the United States minted two-cent and three-cent pieces. Frances
Steib has three times as many three-cent pieces as two-cent pieces, and the face value of
these coins is $2.42. How many of each denomination does she have?
15.In 2010, general admission to the Art Institute of Chicago cost $18 for adults and $12 for
children and seniors. If $22,752 was collected from the sale of 1460 general admission
tickets, how many adult tickets were sold? (Source:www.artic.edu)
16.For a high school production of Annie Get Your Gun, student tickets cost $5 each while
nonstudent tickets cost $8. If 480 tickets were sold for the Saturday night show and a
total of $2895 was collected, how many tickets of each type were sold?
SECTION 2.4 Further Applications of Linear Equations 85
Number
of Coins Denomination Value
x 0.01 0.01x
x
0.25
4.37 TotalNumber
of Coins Denomination Value
x 0.05 0.05x
x
2 x 0.50
2.60 Total