To begin with this question, we must write the translate the written problem into an algebraic problem that can be solved. Remember, "quotient" means division, "times" means multiplication, and "is no more than" is an inequality. Let's start from the beginning:
Our unknown, "a number," will be represented by "x." "The quotient of five times a number and 7" translates to 5x/7. "is no more than" is less than, which we will show using the symbol "<." 10 will remain 10. So, our inequality is 5x/7 < 10. To solve, we will isolate the variable by first multiplying both sides by 7 to get 5x < 70. And finally, we will divide both sides by 5 to get x < 14.