The quotient of a number and -30 is at most -15

Question

Please help algebraic expression write and solve.

Answer 1

First, remember that the word “quotient” refers to the result of a division calculation.

The phrase “The quotient of a number and –30” is another way of saying “A number is divided by –30”.

In the real world nobody talks like this, but math teachers expect us to understand the phrase, and we have to get it right! Because division doesn’t possess the commutative property ORDER MATTERS!

When using this phrasing the first number expressed is the dividend and the second number is the divisor.

For instance, when translating the phrase “The quotient of A and B is C” into algebraic symbols for division we could get A ÷ B = C or A/B = C

(Since this is Algebra 1, you’re probably using the fraction bar to symbolize division.)

Our second challenge is to recognize that the relationship described in this problem is an inequality, NOT and equation. Our quotient is –15 OR smaller.

If we use Q for the quotient, we can set up the inequality as Q / (-30) ≤ -15.

Now we’re ready to solve. Solving inequalities is just like solving equations BUT with one exception.

If you need to multiply or divide by a negative number, you also have to switch the inequality symbol.

To solve this inequality for Q all we have to do is multiply both sides by –30 AND change the ≤ to ≥.

Giving us Q  (-30) × (-15).

Lastly, since a negative time a negative is positive our final answer is Q ≥ 450.

Answer 2

Asked and answered.