Leo needs at least 200 points. He gets 15 points for each game. How… Step by Step

Step by step

The question

Question: Leo needs at least 200 points.

He gets 15 points for each game.

How many games must he play?

1 Find what we know

What do we know?

At least 200 points.

15 points for each game.

What do we want?

How many games.

2 Name the unknown

We don't know how many games.

So we call it x.

x = number of games

At least 200 points means 200 points or more.

We write ≥ 200 points.

at least 200 points → ≥ 200 points

3 Write the inequality

In words: what the games make is at least 200 points.

15x = 200

So the inequality is 15x ≥ 200.

Now we solve it.

15x ≥ 200

4 Remove the 15

15x means 15 times x.

We want just x.

To remove times 15, we divide by 15.

We do it on both sides, so the sign stays true.

15x15 ≥ 20015

15 divided by 15 is 1.

So just x is left.

We can make 200/15 simpler.

It is the same as 40/3.

20015 = 403

So x is greater than or equal to 40/3.

x ≥ 403

5 Show it on a number line

6 Answer the question

That is about 13.33.

403 ≈ 13.33

Games come in whole numbers.

The smallest whole number from 13.33 up is 14.

So we round up.

x ≥ 14

Careful!

13.33 rounds to 13 the usual way.

But 13 games are 195 points.

That is not enough.

So we round up.

Careful: not 13 games ✗

13 × 15 points = 195 points < 200 points

So at least 14 games.

7 Check

Let's check in the story.

14 games: 210 points.

That is at least 200 points.

14 games: 14 × 15 points = 210 points ≥ 200 points

But 13 games would be 195 points: not enough.

So 14 is the fewest.

So the answer is right!

13 games: 13 × 15 points = 195 points < 200 points ✗

Let's look back.

First: find what we know.

Then: name the unknown.

Then: write the inequality.

Then: solve it.

Then: answer the question.

Last: check.

Answer