Question

Which of the following is an example of a word problem for 72 - 12a < 24?

a) If a is a positive integer, solve for a: 72 - 12a = 24.
b) If you have 72 apples and you give away 12a apples, how many apples do you have left when a is a positive number less than 2?
c) Simplify the expression 72 - 12a when a is less than 2.
d) Find the value of a in the equation 72 - 12a = 24.

Answer 1

The word problem for the inequality 72 - 12a < 24 is option b). The steps involve subtracting 72 from both sides, dividing by -12, and considering the conditions on 'a', leading us to conclude that no positive value of 'a' less than 2 satisfies the inequality.

Step-by-step explanation:

An example of a word problem for the inequality 72 - 12a < 24 would be: If you have 72 apples and you give away 12a apples, how many apples do you have left when a is a positive number less than 2? The task here is to determine the range of values for the variable 'a' that would satisfy the given inequality, not to solve for an exact value as we would do in an equation. Solving this inequality involves isolating the variable on one side and interpreting the result.

Let's solve the word problem step by step:

1. Start with the original inequality: 72 - 12a < 24.
2. Subtract 72 from both sides to get -12a < -48.
3. Since we are dealing with an inequality, we need to reverse the inequality sign when we divide both sides by a negative number. So, we divide both sides by -12 to get a > 4.

Since a must be a positive number less than 2, no positive value of a less than 2 will satisfy the inequality as a > 4. Therefore, there are no apples left because we cannot give away 12a apples and still satisfy the inequality 72 - 12a < 24 where a is less than 2.