Quadratic Applications Practice Problems
Practice
 The product of two consecutive odd numbers is 399. Find the numbers.
 The product of two consecutive numbers is 380. Find the numbers.
 The product of two consecutive numbers is 650. Find the numbers.
 The product of two consecutive even numbers is 288. What are the numbers?
 Two numbers differ by 7. Their product is 228. What are the numbers?
Solution

Let x = first number x + 2 = second number
There are two solutions: 19 and 21, and –21 and –19.

Let x = first number x + 1 = second number
x ( x + 1)
= 380
x ^{2} + x
= 380
x ^{2} + x – 380
= 0
( x + 20)( x – 19)
= 0
There are two solutions: 19 and 20, and –19 and –20.

Let x = first number x + 1 = second number
x ( x + 1)
= 650
x ^{2} + x
= 650
x ^{2} + x – 650
= 0
( x – 25)( x + 26)
= 0
There are two solutions: 25 and 26, and –25 and –26.

Let x = first number x + 2 = second number
x ( x + 2)
= 288
x ^{2} + 2 x
= 288
x ^{2} + 2 x – 288
= 0
( x – 16)( x + 18)
= 0
There are two solutions: 16 and 18, and –16 and –18.

Let x = first number x + 7 = second number
x ( x + 7)
= 228
x ^{2} + 7 x
= 228
x ^{2} + 7 x – 228
= 0
( x – 12)( x + 19)
= 0
There are two solutions: 12 and 19, –12 and –19.
Practice problems for this concept can be found at: Algebra Quadratic Applications Practice Test.
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