Final answer:
The phrase 'five times less than the quotient of a number and 3 is -7' can be expressed as the equation 0 - 5 * (x/3) = -7. Solving this equation step by step, we find that the original number is 4.2.
Step-by-step explanation:
The equation "five times less than the quotient of a number and 3 is -7" can be formulated as 5 times a certain value subtracted from this quotient equals -7. To find the quotient, let's denote the unknown number as 'x'. Therefore, the quotient of that number and 3 is x/3. The phrase 'five times less than' means we need to subtract 5 times this quotient from a certain value (often the value itself in mathematics). But since we are dealing with negatives, it can be a bit tricky. Because we are saying 'five times less', we are effectively subtracting this quantity from 0, so the equation can be written as 0 - 5 * (x/3) = -7.
The next step is to solve it:
- Multiply the quotient by 5: 5 * (x/3).
- Since it's 'five times less', subtract from 0: 0 - 5 * (x/3).
- Equate to -7: 0 - 5 * (x/3) = -7.
- Now simplify the equation: -5x/3 = -7.
- Multiply both sides by -3/5 to solve for x: x = (-7) * (-3/5).
- Simplify the right side: x = 21/5 or x = 4.2.
Thus, the original number x is 4.2.