Four times a number equals the number increased by 9.
Let's translate each one of our word sentences into equations:
Four times a number plus 9 is 9.
Let [tex]y[/tex] be the number
Four times a number is [tex]4y[/tex]
Four times the number plus 9 is [tex]4y+9[/tex]
"is 9" means that four times the number plus 9 is equal to nine, so:
[tex]4y+9=9[/tex]
[tex]4y+9=9[/tex] is different to our equation, [tex]4y = y + 9[/tex], so this is not the word sentence that represents our equation.
Four times a number equals the number increased by 9.
Again, let [tex]y[/tex] be the number
Four times a number is [tex]4y[/tex]
The number increased by 9 is [tex]y+9[/tex]
Since both are equal, our equation is: [tex]4y=y+9[/tex]
Look! This is our given equation, so "Four times a number equals the number increased by 9." is the word sentence that represents our equation.
Let's do the last two just for fun:
Four increased by a number equals the number increased by 9.
Let [tex]y[/tex] be the number
Four increased by a number is [tex]4+y[/tex]
the number increased by 9 is [tex]y+9[/tex]
Since both are equal, [tex]4+y=y+9[/tex]
This is not our equation.
Four times the sum of a number and 9 is the number.
Let [tex]y[/tex] be the number
The sum of a number and 9 is [tex]y+9[/tex]
Four times that sum is [tex]4(y+9)[/tex]
Since that sum is equal to the number, [tex]4(y+9)=y[/tex]
This is not our equation.
