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Algebra 2
Section 1.5 B
Number Problems
1. The sum of three consecutive integers is 12 less than
4 times the first integer. What are the three integers?
x = 1st
x + 1 = 2nd
x + 2 = 3rd
sum of three consecutive integers
x + x + 1 + x + 2 = 4x - 12
12 less than 4 times the 1st
3x + 3 = 4x – 12
-3
combine like terms
-3
3x = 4x – 15
- 4x - 4x
-x = -15
x = 15
x + 1 = 16
x + 2 = 17
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2. The population of city A is 4 times the population of city B.
City C has 670 fewer people than city A. What is the population
of each city if their combined population is 8,330?
{x could equal either city B or city A}
If x = city B, then
4x = city A
4x – 670 = city C It may be better to stay
If x = city A, then
x – 670 = city C
x/4 = city B
away from using fractions
B A
C
x + 4x + 4x – 670 = 8330
combined population = 8,330
9x – 670 = 8330
+ 670
+ 670
9x = 9000
x = 1000 (city B)
4x = 4000 (city A)
4x – 670 = 3330 (city C)
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3. There are four consecutive multiples of 3 such that the sum of
the first three multiples is twice the fourth. Find the four
multiples of 3.
x = 1st
x + 3 = 2nd
x + 6 = 3rd
x + 9 = 4th
consecutive multiples of 3
increase by 3 each time
Sum of the first 3
twice the 4th
x + x + 3 + x + 6 = 2(x + 9)
3x + 9 = 2x + 18
-9
-9
3x = 2x + 9
- 2x - 2x
x=9
x + 3 = 12
x + 6 = 15
x + 9 = 18
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4. Twice the sum of three consecutive multiples of 15 is 270.
What are the three multiples of 15?
x = 1st
x + 15 = 2nd
x + 30 = 3rd
consecutive multiples of 15
increase by 15 each time
2(x + x + 15 + x + 30) = 270
2(3x + 45) = 270 combine like terms
6x + 90 = 270 distributive property
- 90
- 90
6x = 180
x = 30
x + 15 = 45
x + 30 = 60
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Solve each problem.
Algebra 2
Section 1.5 B
Assignment
1.) There are three consecutive even integers such that the sum of the
first two is 22 more than the third. Find the three even integers.
2.) A company’s total sales were $150,000 for a 3-year period. Sales for the second
year were $20,000 more than the first year’s sales. The third year’s sales were
3 times those of the second year. Find the sales amount for each year.
3.) The sum of three consecutive multiples of 6 is 30 more than the fifth consecutive
multiple of 6. Find the fourth of these five consecutive multiples of 6.
4.) One-half of the sum of three consecutive multiples of 10 is 75. Find the
three multiples of 10.
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