Answer:
22
Explanation:
Given
From Juan's calculation,
Difference of two positive integers = 2
From Maria's calculation,
Product of same integers = 120
Required
Find the sum of the two numbers
Let the two integers be represented by a and b
a - b = 2 ------- (1)
a * b = 120 ------- (2)
Make a the subject of formula in (1)
a = 2 + b
Substitute 2 + b for a in (2)
(2 + b) * b = 120
Open bracket
2 * b + b * b = 120
2b + b² = 120
Rearrange
b² + 2b = 120
Subtract 120 from both sides
b² + 2b - 120 = 120 - 120
b² + 2b - 120 = 0
At this point, we have a quadratic equation.
We start by expanding the expression
b² + 12b - 10b - 120 = 0
Factorize
b(b + 12) - 10(b + 12) = 0
(b - 10)(b + 12) = 0
This implies that
b - 10 = 0 or b + 12 = 0
Make b the subject of formula in both cases
b = 10 or b = -12
From the question, we understand that both numbers are positive.
This means that
b = -12 will be discarded.
Hence, b = 10
Recall that a = 2 + b
Substitute 10 for b
a = 2 + 10
a = 12
This implies that the two numbers are 12 and 10.
Their sum = 12 + 10
Sum = 22
The correct answer is 22