A lift can carry at most 600 kg. Each box weighs 80 kg. How many… Easy

The question

Question: A lift can carry at most 600 kg.

Each box weighs 80 kg.

How many boxes can it carry?

1 Find what we know

What do we know?

At most 600 kg.

80 kg for each box.

What do we want?

How many boxes.

2 Name the unknown

We don't know how many boxes.

So we call it x.

At most 600 kg means 600 kg or less.

We write ≤ 600 kg.

3 Write the inequality

In words: what the boxes make is at most 600 kg.

So the inequality is 80x ≤ 600.

Now we solve it.

4 Remove the 80

80x means 80 times x.

We want just x.

To remove times 80, we divide by 80.

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

80 divided by 80 is 1.

So just x is left.

We can make 600/80 simpler.

It is the same as 15/2.

So x is less than or equal to 15/2.

5 Show it on a number line

6 Answer the question

15/2 is 7.5.

Boxes come in whole numbers.

The biggest whole number up to 7.5 is 7.

So we round down.

Careful!

7.5 rounds to 8 the usual way.

But 8 boxes are 640 kg.

That is too much.

So we round down.

So at most 7 boxes.

7 Check

Let's check in the story.

7 boxes: 560 kg.

That is not more than 600 kg.

But 8 boxes would be 640 kg: too much.

So 7 is the most.

So the answer is right!

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.

▶ Watch it solved

Sam has $20. He saves $15 each week. He wants to have at least $100… Medium

The question

Question: Sam has $20.

He saves $15 each week.

He wants to have at least $100.

How many weeks must he save?

1 Find what we know

What do we know?

At least $100.

$15 for each week.

At the start: $20.

What do we want?

How many weeks.

2 Name the unknown

We don't know how many weeks.

So we call it x.

At least $100 means $100 or more.

We write ≥ $100.

3 Write the inequality

In words: what the weeks add, plus the start, is at least $100.

So the inequality is 15x + 20 ≥ 100.

Now we solve it.

We want x by itself.

Two things are stuck to x: times 15 and + 20.

The + 20 is on the outside, so it comes off first.

Then the times 15.

4 Remove the + 20

To remove + 20, we take away 20.

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

+ 20 and − 20 make zero.

Cross them out.

100 − 20 = 80.

Now we have 15x ≥ 80.

5 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.

15 divided by 15 is 1.

So just x is left.

We can make 80/15 simpler.

It is the same as 16/3.

So x is greater than or equal to 16/3.

6 Show it on a number line

7 Answer the question

That is about 5.33.

Weeks come in whole numbers.

The smallest whole number from 5.33 up is 6.

So we round up.

Careful!

5.33 rounds to 5 the usual way.

But 5 weeks are $95.

That is not enough.

So we round up.

So at least 6 weeks.

8 Check

Let's check in the story.

6 weeks: $110.

That is at least $100.

But 5 weeks would be $95: not enough.

So 6 is the fewest.

So the answer is right!

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.

▶ Watch it solved

Ben can spend at most $20. Each pen costs $1.50. How many pens can… Harder

The question

Question: Ben can spend at most $20.

Each pen costs $1.50.

How many pens can he buy?

1 Find what we know

What do we know?

At most $20.

$1.50 for each pen.

What do we want?

How many pens.

2 Name the unknown

We don't know how many pens.

So we call it x.

At most $20 means $20 or less.

We write ≤ $20.

3 Write the inequality

In words: what the pens make is at most $20.

So the inequality is 1.5x ≤ 20.

Now we solve it.

4 Remove the decimals

Decimals are hard to work with.

Let's get rid of them.

We multiply every part by 10.

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

10 is a positive number, so the sign stays the same.

Times 10 moves the point 1 place to the right.

10 × 1.5x = 15x.

10 × 20 = 200.

Write the answers.

No more decimals!

5 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.

15 divided by 15 is 1.

So just x is left.

We can make 200/15 simpler.

It is the same as 40/3.

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

6 Show it on a number line

7 Answer the question

That is about 13.33.

Pens come in whole numbers.

The biggest whole number up to 13.33 is 13.

So we round down.

Careful!

At most means we may not go over.

So we always round down.

So at most 13 pens.

8 Check

Let's check in the story.

13 pens: $19.50.

That is not more than $20.

But 14 pens would be $21: too much.

So 13 is the most.

So the answer is right!

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.

▶ Watch it solved