Question

On her math test, Anna is asked to write an inequality that fits the following situation:
The library is having a contest to guess the number of candy pieces in a jar. John’s guess of
three times the number of candy pieces in the jar increased by 100 is a lower number than
Keisha’s guess of 250 less than twice the number of candy pieces.
Anna writes the inequality 3x + 100 < 250 – 2x, which is incorrect.
7. Can you find Anna’s mistake? What is the correct way to write this inequality?

Answer 1

Representing the given information mathematically, we have:

Let the number  of candy pieces in the jar be $x$

Since, it is given that:

John's guess of three times the number of candy pieces in the jar increased by $100$ is lower number than Keisha's guess of 250 less than twice the number of candy pieces.

Going to the John's guess, we get:

$3x+100$

For the Keisha's guess, we have:

$2x-250$

Therefore, according to the question, we get the inequality:

$3x+100<2x-250$

Anna did the mistake in comprehending the right side of the inequality correctly. Instead of comprehending $2x-250$ she wrote: $250-2x$ (which is incorrect).

Thus, the correct inequality is:

$3x+100<2x-250$