Worked examples
The question
Question: 5 more than twice a number is 17.
Find the number.
1 Find what we know
What do we know?
5 more than twice a number is 17.
What do we want?
The number.
2 Name the unknown
We don't know the number.
So we call it x.
x = the number
3 Write the equation
Change the words to math, one part at a time.
2x + 5 = 17
We start with twice a number, then add 5.
So the equation is 2x + 5 = 17.
Now we solve it.
2x + 5 = 17
We want x by itself.
Two things are stuck to x: times 2 and + 5.
The + 5 is on the outside, so it comes off first.
Then the times 2.
4 Remove the + 5
To remove + 5, we take away 5.
We do it on both sides, so they stay equal.
2x + 5 − 5 = 17 − 5
+ 5 and − 5 make zero.
Cross them out.
17 − 5 = 12.
17 − 5 = 12
Now we have 2x = 12.
2x = 12
5 Remove the 2
2x means 2 times x.
We want just x.
To remove times 2, we divide by 2.
We do it on both sides, so they stay equal.
2x2 = 122
2 divided by 2 is 1.
So just x is left.
12 divided by 2 is 6.
122 = 6
So x = 6!
x = 6
6 Answer the question
The number is 6.
7 Check
Let's check in the story.
Put 6 in the story: 5 more than twice 6.
5 more than twice 6
It makes 17, like the story says.
So the answer is right!
2(6) + 5 = 12 + 5 = 17
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
The question
Question: The sum of three consecutive numbers is 48.
Find the numbers.
1 Find what we know
What do we know?
Consecutive means in a row.
Three numbers in a row, like 5, 6, 7.
Each one is 1 more than the one before.
Added together, they make 48.
What do we want?
The 3 numbers.
2 Name the unknown
We don't know the first number.
So we call it x.
x = first number
The second number is 1 more: x + 1.
x + 1 = second number
The third number is 1 more again: x + 2.
x + 2 = third number
3 Write the equation
In words: first plus second plus third makes the sum.
x + (x + 1) + (x + 2) = 48
So the equation is x + (x + 1) + (x + 2) = 48.
Now we solve it.
x + (x + 1) + (x + 2) = 48
4 Open the brackets
A bracket with a plus or nothing in front can just be removed.
x + x + 1 + x + 2 = 48
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.
Plain numbers go together.
x + x + x = 3x.
1 + 2 = 3.
x + x + x = 3x
1 + 2 = 3
Now we have 3x + 3 = 48.
3x + 3 = 48
We want x by itself.
Two things are stuck to x: times 3 and + 3.
The + 3 is on the outside, so it comes off first.
Then the times 3.
6 Remove the + 3
To remove + 3, we take away 3.
We do it on both sides, so they stay equal.
3x + 3 − 3 = 48 − 3
+ 3 and − 3 make zero.
Cross them out.
48 − 3 = 45.
48 − 3 = 45
Now we have 3x = 45.
3x = 45
7 Remove the 3
3x means 3 times x.
We want just x.
To remove times 3, we divide by 3.
We do it on both sides, so they stay equal.
3x3 = 453
3 divided by 3 is 1.
So just x is left.
45 divided by 3 is 15.
453 = 15
So x = 15!
x = 15
8 Answer the question
The second number is x + 1: 15 + 1 = 16.
x + 1 = 15 + 1 = 16
The third number is x + 2: 15 + 2 = 17.
x + 2 = 15 + 2 = 17
The numbers are 15, 16 and 17.
9 Check
Let's check in the story.
Add the numbers: they make 48, like the story says.
15 + 16 + 17 = 48
And they are in a row, 1 apart.
15, 16, 17: in a row
Does it make sense?
48 shared by 3 is 16.
Our numbers are close to 16.
So the answer is right!
makes sense: 48 ÷ 3 = 16, near 15, 16 and 17
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
The question
Question: The sum of four consecutive numbers is 90.
Find the numbers.
1 Find what we know
What do we know?
Consecutive means in a row.
Four numbers in a row, like 5, 6, 7, 8.
Each one is 1 more than the one before.
Added together, they make 90.
What do we want?
The 4 numbers.
2 Name the unknown
We don't know the first number.
So we call it x.
x = first number
The second number is 1 more: x + 1.
x + 1 = second number
The third number is 1 more again: x + 2.
x + 2 = third number
The fourth number is 1 more again: x + 3.
x + 3 = fourth number
3 Write the equation
In words: first plus second plus third plus fourth makes the sum.
x + (x + 1) + (x + 2) + (x + 3) = 90
So the equation is x + (x + 1) + (x + 2) + (x + 3) = 90.
Now we solve it.
x + (x + 1) + (x + 2) + (x + 3) = 90
4 Open the brackets
A bracket with a plus or nothing in front can just be removed.
x + x + 1 + x + 2 + x + 3 = 90
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.
Plain numbers go together.
x + x + x + x = 4x.
1 + 2 + 3 = 6.
x + x + x + x = 4x
1 + 2 + 3 = 6
Now we have 4x + 6 = 90.
4x + 6 = 90
We want x by itself.
Two things are stuck to x: times 4 and + 6.
The + 6 is on the outside, so it comes off first.
Then the times 4.
6 Remove the + 6
To remove + 6, we take away 6.
We do it on both sides, so they stay equal.
4x + 6 − 6 = 90 − 6
+ 6 and − 6 make zero.
Cross them out.
90 − 6 = 84.
90 − 6 = 84
Now we have 4x = 84.
4x = 84
7 Remove the 4
4x means 4 times x.
We want just x.
To remove times 4, we divide by 4.
We do it on both sides, so they stay equal.
4x4 = 844
4 divided by 4 is 1.
So just x is left.
84 divided by 4 is 21.
844 = 21
So x = 21!
x = 21
8 Answer the question
The second number is x + 1: 21 + 1 = 22.
x + 1 = 21 + 1 = 22
The third number is x + 2: 21 + 2 = 23.
x + 2 = 21 + 2 = 23
The fourth number is x + 3: 21 + 3 = 24.
x + 3 = 21 + 3 = 24
The numbers are 21, 22, 23 and 24.
9 Check
Let's check in the story.
Add the numbers: they make 90, like the story says.
21 + 22 + 23 + 24 = 90
And they are in a row, 1 apart.
21, 22, 23, 24: in a row
Does it make sense?
90 shared by 4 is about 23.
Our numbers are close to 23.
So the answer is right!
makes sense: 90 ÷ 4 ≈ 23, near 21, 22, 23 and 24
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
