Answer :
[tex]x-\ yellow\ cars\\\\
9x-\ white\ cars\\\\
x+9x=40\\\\
10x=40\ \ \ |Divide\ by\ 10\\\\
x=4\\\\
There\ were\ 4\ yellow\ cars\ and\ 36\ white\ cars.[/tex]
The number of white cars that Rafeal counted is [tex]\boxed{\bf 36}[/tex].
Further explanation:
It is given that the total number of white and yellow cars is [tex]40[/tex] and the number of white cars is [tex]9\text{ times}[/tex] the number of yellow cars.
Suppose the number of white cars is denoted by [tex]x[/tex] and the number of yellow cars is denoted by [tex]y[/tex].
Now we can form two equation with the given information.
The sum of the white and yellow cars is [tex]40[/tex] that means the summation of [tex]x[/tex] and [tex]y[/tex] is [tex]40[/tex] and in the equation form it can be written as follows:
[tex]\boxed{x+y=40}[/tex] .....(1)
Now for the formation of second equation the information which is given is the white cars are [tex]9\text{ times}[/tex] as many as yellow cars. So the second equation is formed as follows:
[tex]\boxed{x=9y}[/tex] .....(2)
Now substitute the value of [tex]x[/tex] from equation (2) to equation (1) to obtain the value of [tex]y[/tex] as follows:
[tex]\begin{aligned}9y+y&=40\\10y&=40\\y&=\dfrac{40}{10}\\y&=4\end{aligned}[/tex]
From the above calculation the value of [tex]y[/tex] is [tex]4[/tex] which means the number of yellow car is [tex]4[/tex].
Now substitute the above value of [tex]y[/tex] in equation (2) to obtain the value of [tex]x[/tex] as follows:
[tex]\begin{aligned}x&=9y\\&=9\cdot 4\\&=36\end{aligned}[/tex]
Therefore, the value of [tex]x[/tex] is [tex]36[/tex].
This implies that the total number of white cars is [tex]36[/tex].
From the above solution it is concluded that the number of white cars counted by Rafael is [tex]\boxed{\bf 36}[/tex].
Learn more:
1. Learn more about the simplified form: https://brainly.com/question/1602237
2. Problem on equation: https://brainly.com/question/4691222
3. Problem on to find the value in an equation: https://brainly.com/question/1900154
Answer details:
Grade: Middle school
Subject: Mathematics
Chapter: Linear equations
Keywords: Equation, white car, yellow car, counting, number, Rafael, total, variables, x, y, 40, 9, summation, substitution, division, notation, nine times.
