Sales for a company were 6 million dollars more the second year than the first, and sales for the third year were tripled the sales for the second year. If sales for the third year were 24 million dollars, what were sales, in millions of dollars, for the first year?
Answers
Sales for the first year were 2 millions of dollars
Further explanationSolving linear equation mean calculating the unknown variable from the equation.
Let the linear equation : y = mx + c
If we draw the above equation on Cartesian Coordinates , it will be a straight line with :
m → gradient of the line
( 0 , c ) → y - intercept
Gradient of the line could also be calculated from two arbitrary points on line ( x₁ , y₁ ) and ( x₂ , y₂ ) with the formula :
[tex]\large {\boxed {m = \frac{y_2 - y_1}{x_2 - x_1}}[/tex]
If point ( x₁ , y₁ ) is on the line with gradient m , the equation of the line will be :
[tex]\large {\boxed {y - y_1 = m ( x - x_1 )}}[/tex]
Let us tackle the problem!
Let:
Sales for the first year = s₁
Sales for the second year = s₂
Sales for the third year = s₃
Given:
s₂ = 6 + s₁
s₃ = 3s₂
s₃ = 24
Unknown:
s₁ = ?
Solution:
[tex]s_3 = 3s_2[/tex]
[tex]24 = 3s_2[/tex]
[tex]s_2 = 24 \div 3[/tex]
[tex]s_2 = 8[/tex]
[tex]s_2 = 6 + s_1[/tex]
[tex]8 = 6 + s_1[/tex]
[tex]s_1 = 8 - 6[/tex]
[tex]s_1 = 2[/tex]
Conclusion:Sales for the first year = 2 millions of dollars
Learn moreInverse of Function : https://brainly.com/question/9289171Rate of Change : https://brainly.com/question/11919986Graph of Function : https://brainly.com/question/7829758Answer detailsGrade: High School
Subject: Mathematics
Chapter: Function
Keywords: Function , Trigonometric , Linear , Quadratic
The sales in the first year is [tex]\boxed{2{\text{million of dollars}}}.[/tex]
Further explanation:
The linear equation with slope m and intercept c is given as follows.
[tex]\boxed{y = mx + c}[/tex]
The standard form of the linear equation can be expressed as follows,
[tex]\boxed{ax + by = c}[/tex]
The formula for slope of line with points [tex]\left( {{x_1},{y_1}} \right)[/tex] and [tex]\left( {{x_2},{y_2}} \right)[/tex] can be expressed as,
[tex]\boxed{m = \frac{{{y_2} - {y_1}}}{{{x_2} - {x_1}}}}[/tex]
Explanation:
Consider the sale in the first year as [tex]x[/tex].
Consider the sale in the second year as [tex]y[/tex].
Consider the sale in the third year as [tex]z[/tex].
Sales for a company were 6 million dollars more the second year than the first.
[tex]y = 6 + x[/tex]
Sales for the third year were 24 million dollars.
[tex]z = 24[/tex]
Sales for the third year were tripled the sales for the second year.
[tex]z = 3y[/tex]
Substitute 24 for z in above equation.
[tex]\begin{aligned}24&= 3y\\\frac{{24}}{3} &= y\\8&= y\\\end{aligned}[/tex]
Substitute [tex]8[/tex] for [tex]\text{y}[/tex] in equation [tex]y = 6 + x[/tex]
[tex]\begin{aligned}8&= 6+ x\\8 - 6&= x\\2&= x\\\end{aligned}[/tex]
The sales in the first year is [tex]\boxed{2{\text{million of dollars}}}.[/tex]
Learn more:
Learn more about inverse of the function https://brainly.com/question/1632445. Learn more about equation of circle brainly.com/question/1506955. Learn more about range and domain of the function https://brainly.com/question/3412497
Answer details:
Grade: High School
Subject: Mathematics
Chapter: Linear inequality
Keywords: sales, company, 6 million, dollars, second year, first, sales for second, sales for third year, tripled, first year, 24 million, millions of dollars.
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