Zoe needs at least 75 points. She gets 8 points for each answer. How… Step by Step

Step by step

The question

Question: Zoe needs at least 75 points.

She gets 8 points for each answer.

How many answers must she get?

1 Find what we know

What do we know?

At least 75 points.

8 points for each answer.

What do we want?

How many answers.

2 Name the unknown

We don't know how many answers.

So we call it x.

x = number of answers

At least 75 points means 75 points or more.

We write ≥ 75 points.

at least 75 points → ≥ 75 points

3 Write the inequality

In words: what the answers make is at least 75 points.

8x = 75

So the inequality is 8x ≥ 75.

Now we solve it.

8x ≥ 75

4 Remove the 8

8x means 8 times x.

We want just x.

To remove times 8, we divide by 8.

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

8x8 ≥ 758

8 divided by 8 is 1.

So just x is left.

So x is greater than or equal to 75/8.

x ≥ 758

5 Show it on a number line

6 Answer the question

That is about 9.38.

758 ≈ 9.38

Answers come in whole numbers.

The smallest whole number from 9.38 up is 10.

So we round up.

x ≥ 10

Careful!

9.38 rounds to 9 the usual way.

But 9 answers are 72 points.

That is not enough.

So we round up.

Careful: not 9 answers ✗

9 × 8 points = 72 points < 75 points

So at least 10 answers.

7 Check

Let's check in the story.

10 answers: 80 points.

That is at least 75 points.

10 answers: 10 × 8 points = 80 points ≥ 75 points

But 9 answers would be 72 points: not enough.

So 10 is the fewest.

So the answer is right!

9 answers: 9 × 8 points = 72 points < 75 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