A car drives at 60 km/h. How many hours does it take to drive 180 km? Easy

The question

Question: A car drives at 60 km/h.

How many hours does it take to drive 180 km?

1 Find what we know

What do we know?

The car goes 60 km in each hour.

The trip is 180 km.

What do we want?

How many hours.

2 Name the unknown

We don't know how many hours.

So we call it x.

How far we go: speed times time.

60 km/h means 60 km in each hour.

3 Write the equation

In words: speed times time makes the distance.

So the equation is 60x = 180.

Now we solve it.

4 Remove the 60

60x means 60 times x.

We want just x.

To remove times 60, we divide by 60.

We do it on both sides, so they stay equal.

60 divided by 60 is 1.

So just x is left.

180 divided by 60 is 3.

So x = 3!

5 Answer the question

So it takes 3 hours.

6 Check

Let's check in the story.

3 hours at 60 km/h: 3 times 60 is 180 km, like the story says.

So the answer is right!

Let's look back.

First: find what we know.

Then: name the unknown.

Then: write the equation.

Then: solve it.

Then: answer the question.

Last: check.

▶ Watch it solved

Plumber A charges $40 plus $20 per hour. Plumber B charges $30 per… Medium

The question

Question: Plumber A charges $40 plus $20 per hour.

Plumber B charges $30 per hour.

After how many hours do they cost the same?

1 Find what we know

What do we know?

Plumber A: $40 one time, plus $20 for each hour.

Plumber B: $30 for each hour.

What do we want?

How many hours make the two costs the same.

2 Name the unknown

We don't know how many hours.

So we call it x.

Plumber A: $20 for each hour, so x hours cost 20x.

Plus $40 one time: 20x + 40.

Plumber B: $30 for each hour, so x hours cost 30x.

3 Write the equation

In words: Plumber A's cost is the same as Plumber B's cost.

So the equation is 20x + 40 = 30x.

Now we solve it.

4 Get x on one side

There is x on both sides.

We want x on one side only.

So we remove the 20x from the left side.

To remove 20x, we take away 20x.

We do it on both sides, so they stay equal.

20x and − 20x make zero.

Cross them out.

30x − 20x = 10x.

Now we have 40 = 10x.

Let's swap the two sides, so x is on the left.

5 Remove the 10

10x means 10 times x.

We want just x.

To remove times 10, we divide by 10.

We do it on both sides, so they stay equal.

10 divided by 10 is 1.

So just x is left.

40 divided by 10 is 4.

So x = 4!

6 Answer the question

So after 4 hours, they cost the same.

7 Check

Let's check in the story.

Plumber A: $40 + 4 × $20 = $120.

Plumber B: 4 × $30 = $120.

The same cost, like the story says.

So the answer is right!

Let's look back.

First: find what we know.

Then: name the unknown.

Then: write the equation.

Then: solve it.

Then: answer the question.

Last: check.

▶ Watch it solved

A café sold 50 drinks. Small drinks cost $2 and large drinks cost… Harder

The question

Question: A café sold 50 drinks.

Small drinks cost $2 and large drinks cost $3.

The café made $130.

How many of each drink were sold?

1 Find what we know

What do we know?

50 drinks in all.

Two kinds: small drinks cost $2 each, large drinks cost $3 each.

All the money: $130.

What do we want?

How many small drinks, and how many large drinks.

2 Name the unknown

We don't know how many small drinks.

So we call it x.

The rest are large.

50 in all, take away the x small ones: 50 − x.

For example: if 5 were small, then 50 − 5 = 45 would be large.

So we need only one letter.

Let's put it in a table: how many, the price, and the money.

Small: x drinks at $2 each.

Large: 50 − x drinks at $3 each.

Money = how many times the price.

2 times x is 2x.

3 times all of 50 − x is 3(50 − x).

We keep 50 − x together in brackets.

The total row: 50 drinks in all, and $130 in all.

3 Write the equation

In words: the small money plus the large money makes all the money.

So the equation is 2x + 3(50 − x) = 130.

Now we solve it.

4 Open the brackets

The 3 in front of the bracket multiplies every part inside.

So we write 3 times each part.

Work out each multiplication.

5 Group like terms

Terms are the parts between the + and − signs.

Like terms are the same kind: same letters, same powers.

All the x terms go together.

2x − 3x = −x.

Now we have −x + 150 = 130.

6 Remove the + 150

We want x by itself.

The + 150 is in the way.

To remove + 150, we take away 150.

We do it on both sides, so they stay equal.

+ 150 and − 150 make zero.

Cross them out.

130 − 150 = −20.

Now we have −x = −20.

7 Remove the −1

−x means −1 times x.

We want just x.

To remove times −1, we divide by −1.

We do it on both sides, so they stay equal.

−1 divided by −1 is 1.

So just x is left.

−20 divided by −1 is 20.

So x = 20!

8 Answer the question

Large: 50 − x.

50 − 20 = 30.

So 20 small drinks and 30 large drinks.

9 Check

Let's check in the story.

20 + 30 = 50 drinks, like the story says.

The money: $40 plus $90 makes $130, like the story says.

Does it make sense?

Both are whole numbers from 0 to 50.

That fits 50 drinks.

So the answer is right!

Let's look back.

First: find what we know.

Then: name the unknown.

Then: write the equation.

Then: solve it.

Then: answer the question.

Last: check.

▶ Watch it solved