Final answer:
The solution to the given equation 'the quotient of a number increased by 4 and -3 is 15' is found by translating the statement into an algebraic equation and solving for x, resulting in the unknown number being -49.
Step-by-step explanation:
The question involves solving an algebraic equation to find the unknown number. According to the statement, 'the quotient of a number increased by 4 and -3 is 15', we can write the equation as (x + 4) / -3 = 15.
Let us solve this step by step:
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Therefore, the unknown number is -49.