The number that Dennis started with is 24
Further explanation
Solving 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 {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]y - y_1 = m ( x - x_1 )[/tex]
Let us tackle the problem.
Let :
The number that Dennis started with is X
If he adds 0.5 to that number and then multiplies the new result by 4 , then:
[tex]( X + 0.5 ) \times 4[/tex]
If he then subtracts 2 and divides the number by 2 , then:
[tex]\frac{[ ( X + 0.5 ) \times 4 ] - 2}{2}[/tex]
If his final answer is 48 , then :
[tex]\frac{[ ( X + 0.5 ) \times 4 ] - 2}{2} = 48[/tex]
[tex][ ( X + 0.5 ) \times 4 ] - 2 = 48 \times 2[/tex]
[tex]( X + 0.5 ) \times 4 = 48 \times 2 + 2[/tex]
[tex]( X + 0.5 ) \times 4 = 96 + 2[/tex]
[tex]( X + 0.5 ) \times 4 = 98[/tex]
[tex]( X + 0.5 ) = \frac{98}{4}[/tex]
[tex]( X + 0.5 ) = \frac{49}{2}[/tex]
[tex]X = \frac{49}{2} - \frac{1}{2}[/tex]
[tex]X = \frac{48}{2}[/tex]
[tex]\large {\boxed {X = 24} }[/tex]
Learn more
- Infinite Number of Solutions : https://brainly.com/question/5450548
- System of Equations : https://brainly.com/question/1995493
- System of Linear equations : https://brainly.com/question/3291576
Answer details
Grade: High School
Subject: Mathematics
Chapter: Linear Equations
Keywords: Linear , Equations , 1 , Variable , Line , Gradient , Point
