Answer:
See Explanation
Step-by-step explanation:
Solving (a): The Variables
The variables are the ages of Jaime, Crystal and Marissa;
Let
x represents Jaime's age;
y represents Crystal's age;
z represents Marissa's age
Solving (b): Equation
[tex]x = 3 + y[/tex]
[tex]z = 2x[/tex]
[tex]x + y + z = 45[/tex]
Solving (c): Result of the equations
[tex]x = 3 + y[/tex] -- (1)
[tex]z = 2x[/tex] -- (2)
[tex]x + y + z = 45[/tex] -- (3)
Make y the subject in (1)
[tex]y = x - 3[/tex]
Substitute [tex]y = x - 3[/tex] and [tex]z = 2x[/tex] in (3)
[tex]x + y + z = 45[/tex]
[tex]x + x - 3 + 2x = 45[/tex]
Collect Like Terms
[tex]x + x + 2x = 45 + 3[/tex]
[tex]4x= 48[/tex]
Solve for x
[tex]x = 48/4[/tex]
[tex]x = 12[/tex]
Substitute [tex]x = 12[/tex] in [tex]y = x - 3[/tex] and [tex]z = 2x[/tex]
[tex]y = x - 3[/tex]
[tex]y= 12 - 3[/tex]
[tex]y = 9[/tex]
[tex]z = 2x[/tex]
[tex]z = 2 * 12[/tex]
[tex]z = 24[/tex]
This implies that;
Jaime is 12; Crystal is 9 and Marissa is 24 years old
Solving (d): Essence of the question
The question asks that we solve for the ages of Jaime, Crystal and Marissa
