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Rafael counted a total of 40 white cars and yellow cars.there were 9 times as many white cars and yellow.how many white cars did Rafeal count


Sagot :

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[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.