Find two whole numbers whose sum is 27 and product is 182. a)15,12 b)14,13c)16,11 d)17,10
Answers
Answer:
b
Step-by-step explanation:
a + b = 27
ab = 182
b = 27 - a
a(27 - a) = 182
27a - a^2 - 182 = 0
-a^2 + 27a - 182 = 0
use quadratic equation:
a = 13 or 14
answer is b
Given : two whole numbers whose sum is 27 and product is 182.
To Find : numbers
a)15,12 b)14,13c)16,11 d)17,10
Solution:
Let say two numbers are
x & y
x + y = 27
=> y = 27 - x
xy = 182
=> x (27 - x) = 182
=> 27x - x² = 182
=> x² - 27x + 182 = 0
using middle term split
=> x² - 13x - 14x + 182 = 0
=> x(x - 13) - 14(x - 13) = 0
=> (x - 13)(x-14) = 0
=> x = 13 , x = 14
y = 27 - x
=> if x = 13 then y = 27 - 13 = 14 ( 13 , 14 are two numbers )
or
=> if x = 14 then y = 27 - 14 = 13 ( 14 , 13 are two numbers )
Hence two numbers are 14 & 13 - option B is correct
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