Question

TUTTI

Jaime is 3 years older than Crystal.
Marissa is twice as old Jaime. The sum
of their ages is 45. How old is each
person?
a) Define a variable:
b) Write an equation.
c) Solve the equation.
d) Answer what is being asked in a
complete sentence.

Answer 1

See Explanation

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

`x = 3 + y`

`z = 2x`

`x + y + z = 45`

Solving (c): Result of the equations

`x = 3 + y` -- (1)

`z = 2x` -- (2)

`x + y + z = 45` -- (3)

Make y the subject in (1)

`y = x - 3`

Substitute
`y = x - 3` and
`z = 2x` in (3)

`x + y + z = 45`

`x + x - 3 + 2x = 45`

Collect Like Terms

`x + x + 2x = 45 + 3`

`4x= 48`

Solve for x

`x = 48/4`

`x = 12`

Substitute
`x = 12` in
`y = x - 3` and
`z = 2x`

`y = x - 3`

`y= 12 - 3`

`y = 9`

`z = 2x`

`z = 2 * 12`

`z = 24`

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