39.In a certain triangle, the measure of the second angle is greater than three times the
first. The third angle measure is equal to the sum of the measures of the other two. Find
the measures of the three angles.
40.The measure of the largest angle of a triangle is 12° less than the sum of the measures of
the other two. The smallest angle measures 58° less than the largest. Find the measures of
the angles.
41.The perimeter of a triangle is 70 cm. The longest side is 4 cm less than the sum of the
other two sides. Twice the shortest side is 9 cm less than the longest side. Find the length
of each side of the triangle.
42.The perimeter of a triangle is 56 in. The longest side measures 4 in. less than the sum of
the other two sides. Three times the shortest side is 4 in. more than the longest side. Find
the lengths of the three sides.
43.In the 2008 Summer Olympics in Beijing, China, Russia
earned 5 fewer gold medals than bronze. The number of
silver medals earned was 35 less than twice the number of
bronze medals. Russia earned a total of 72 medals. How
many of each kind of medal did Russia earn? (Source:
World Almanac and Book of Facts.)
44.In a random sample of Americans of
voting age conducted in 2010, 8% more
people identified themselves as Inde-
pendents than as Republicans, while 6%
fewer people identified themselves as
Republicans than as Democrats. Of
those sampled, 2% did not identify with
any of the three categories. What percent
of the people in the sample identified
themselves with each of the three politi-
cal affiliations? (Source:Gallup, Inc.)
10°
SECTION 4.3 Applications of Systems of Linear Equations 245
x°y°z°y°x° z°Solve each problem by using three variables. See Examples 5 and 6.(In Exercises 37 – 40,
remember that the sum of the measures of the angles of a triangle is 180°.)
37.In the figure, and
. Determine a third equation involv-
ing x, y, and z, and then find the meas-
ures of the three angles.
38.In the figure, xis 10 less than yand
20 less than z. Write a system of equa-
tions and find the measures of the three
angles.100
z=x+ 10 x+y =45.Tickets for the Harlem Globetrotters show at Michigan State University in 2010 cost $16,
$23, or, for VIP seats, $40. If nine times as many $16 tickets were sold as VIP tickets, and
the number of $16 tickets sold was 55 more than the sum of the number of $23 tickets and
VIP tickets, sales of all three kinds of tickets would total $46,575. How many of each kind
of ticket would have been sold? (Source:Breslin Student Events Center.)
46.Three kinds of tickets are available for a Cowboy Mouthconcert: “up close,” “in the mid-
dle,” and “far out.” “Up close” tickets cost $10 more than “in the middle” tickets, while
“in the middle” tickets cost $10 more than “far out” tickets. Twice the cost of an “up
close” ticket is $20 more than 3 times the cost of a “far out” ticket. Find the price of each
kind of ticket.