Answer :
Solution: The number of white cars counted by Rafael is 36.
Explanation:
Let the number of white cars be x and number of yellow cars be y.
It is given that the total number of yellow and white cars counted by rafael is 40.
[tex]x+y=40[/tex] .....(1)
According to the given information he counts 9 times as many white cars as yellow car. It means the number of white cars counted by rafael is 9 times of the yellow cars.
[tex]x=9y[/tex] ......(2)
Put [tex]x=9y[/tex] in equation (1).
[tex]9y+y=40\\10y=40\\y=4[/tex]
Put [tex]y=4[/tex] in equation (1).
[tex]x+4=40\\x=36[/tex]
Since x is the number of white cars, therefore number of white cars counted by Rafael is 36.
White cars did Rafael count = 36 cars
Further explanation
A two-variable linear equation system is an equation that involves 2 variables (the value that can change) and the equation has the highest rank of 1
In this equation system there are coefficients and variables whose solutions can use:
- 1. substitution
- 2. elimination
- 3. graph
- 4. mix
Steps for completion with the substitution method:
- 1. change one of the equations to the form y = ax + b or x = ay + b
- 2. substitution the value of x / y to another equation
- 3. solve the equation
- 4. substitution results from point 3 in one equation
In the statement of the question mentioned Rafael counted the number of white cars and yellow cars = 40 pieces so that the equation:
w + y = 40 ---- equation 1
w = white car
y = yellow car
Then Rafael concluded that white cars were nine times the yellow cars, so the equation was
w = 9y ... equation 2
So that the solution
- 1. equation 2, we enter into equation 1
9y + y = 40
10 y = 40
y = 4
- 2. We enter the value of y into one of the equations
w = 9y
w = 9.4
w = 36
So we get 36 white cars
Learn more
the substitution method
https://brainly.com/question/11705106
https://brainly.com/question/7162056
The work of a student to solve a set of equations
https://brainly.com/question/10589573
Keywords: the substitution method, elimination, graph, a two-variable linear equation system