An equation is formed when two equal expressions. The sum of the two integers is 23. The correct option is B, 23.
What is an equation?
An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
Let the first positive integer be represented by a and the other positive integer be represented by b.
Given that one positive integer is 3 greater than 4 times another positive integer. Therefore, the equation for the given statement can be formed as shown below.
a = 3 + 4b
It is also given that the product of the two integers is 76. Therefore, the product of the two integers can be written as,
a × b = 76
Substitute the value of a,
(3 + 4b) × b = 76
3b + 4b² = 76
4b² + 3b - 76 = 0
4b² + 19b - 16b - 76 = 0
b(4b + 19) - 4(4b + 19) = 0
(b - 4)(4b + 19) = 0
b = (-19/4), 4
Since the integer is positive, therefore, the value of b will be 4.
Now, the value of a can be written as,
a = 3 + 4b
a = 3 + 4(4)
a = 19
Further, the sum of the two integers can be written as,
a + b = 19 + 4 = 23
Hence, the sum of the two integers is 23.
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