Question

You are playing a video game. For each diamond you collect, you earn 100 points. You also earn 75 bonus points by completing the level in less than 2 minutes. You need to earn more than 1575 points to continue on to the next level. Write and solve an inequality that represents the numbers d of diamonds you must collect in less than 2 minutes to advance to the next level.

Answer 1

The data that we have is:

For each diamond, you earn 100 points.

If you complete the level in less than 2 minutes, you earn a bonus of 75 points.

You want to earn more than 1575 points.

Now, assuming that you want to write and solve n inequality that represents the numbers d of diamonds you must collect in less than 2 minutes to advance to the next level.

Because you end in less than 2 minutes, then you have the bonus of 75 points.

Then the number of points as a function of d, the number of diamonds, is:

P(d) = 100*d + 75

And you want that:

P(d) > 1575

100*d + 75 > 1575

Now we can solve this for d.

100d > 1575 - 75

100d > 1500

d > 1500/100

d > 15

You must collect more than 15 diamonds.