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Algebra 2
Section 3.7 B
More Number Problems
1. One number is 4 less than another number. Their product is 21.
Find all such pairs of numbers.
x = one number
x – 4 = other number
x(x – 4) = 21
x2 – 4x = 21
-21 -21
x2 – 4x – 21 = 0 standard form
(x – 7)(x + 3) = 0 factor into 2 binomials
x – 7 = 0 or x + 3 = 0 set each factor equal to 0
+7 +7
x=7
x–4=3
-3
or
-3
x = -3
x – 4 = -7
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2. The product of two numbers is 9, and one number is 4 times the
other number. Find the two numbers.
x = one number
4x = other number
x(4x) = 9
4x2 = 9
-9
-9
4x2 – 9 = 0
(2x + 3)(2x – 3) = 0 4x2 – 9 is a difference of 2 squares
2x + 3 = 0 or 2x – 3 = 0 set each factor equal to 0
+3 +3
-3 -3
2x = -3
x = -3/2
4x = -6
or
2x = 3
x = 3/2
4x = 6
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3. Find three consecutive multiples of 5 so that the product of the first
and the third numbers is 200.
x = 1st
x + 5 = 2nd
x + 10 = 3rd
x(x + 10) = 200
x2 + 10x = 200
-200 -200
x2 + 10x – 200 = 0 standard form
(x + 20)(x – 10) = 0 factor into 2 binomials
x + 20 = 0 or x – 10 = 0 set each factor equal to 0
-20 -20
x = -20
x + 5 = -15
x + 10 = -10
+10 +10
or
x = 10
x + 5 = 15
x + 10 = 20
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Solve each problem.
Algebra 2
Section 3.7 B
Assignment
1.) Forty-four students are seated in rows in a lecture hall. The number of students in each
row is 7 more than the number of rows. Find the number of students seated in each row.
2.) An album contains 1.020 stamps. How many pages are in the album if the number
of pages is 8 more than 4 times the number of stamps on each page?
3.) The product of two numbers is 33. One number is 2 more than 3 times the other number.
Find the numbers.
4.) Find two numbers whose product is 25 if one number is 9 times the other number.
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