39.Two angles whose sum is are called
complementary angles.Find the meas-
ures of the complementary angles shown
in the figure.
40.Two angles whose sum is are called
supplementary angles.Find the meas-
ures of the supplementary angles shown
in the figure.
90° 180°
88 CHAPTER 2 Linear Equations, Inequalities, and Applications
(2x)°
(5x – 1)° (3x + 5)° (5x + 15)°
Consecutive Integer Problems
Consecutive integersare integers that follow each other in counting order, such
as 8, 9, and 10. Suppose we wish to solve the following problem:
Find three consecutive integers such that the sum of the first and third,
increased by 3,is 50 more than the second.
Let x the first of the unknown integers, the second, and
the third. We solve the following equation.
Sum of the increased 50 more than
first and third by 3 is the second.
The solution of this equation is 46, so the first integer is , the second
is , and the third is. The three integers are 46, 47, and
48. Check by substituting these numbers back into the words of the original
problem.
x+ 1 = 47 x+ 2 = 48
x= 46
x= 46
2 x+ 5 = x+ 51
x+ 1 x+ 22 + 3 = 1 x+ 12 + 50
= x+ 1 = x+ 2 =
Solve each problem involving consecutive integers.
41.Find three consecutive integers such that the sum of the first and twice the second is 17
more than twice the third.
42.Find four consecutive integers such that the sum of the first three is 54 more than the
fourth.
43.If I add my current age to the age I will be next year on this date, the sum is 103 yr. How
old will I be 10 yr from today?
44.Two pages facing each other in this book have 193 as the sum of their page numbers.
What are the two page numbers?
45.Find three consecutive evenintegers such that the sum of the least integer and the middle
integer is 26 more than the greatest integer.
46.Find three consecutive evenintegers such that the sum of the least integer and the greatest
integer is 12 more than the middle integer.
47.Find three consecutive oddintegers such that the sum of the least integer and the middle
integer is 19 more than the greatest integer.
48.Find three consecutive oddintegers such that the sum of the least integer and the greatest
integer is 13 more than the middle integer.
