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(23)
15+0.08 t > 3+0.12 t
(3)
15 t+0.08 < 3t+0.12
(4)
15 t+0.08 > 3t+0.12
5. Show work for the following question (3 points)
Julia is 4 years older than twice Kelly's age,
x. The product of their ages is 96 . Write an equation that models this situation.
Determine Kelly's age algebraically.

( $23$ ) $15+0.08 t>3+0.12 t$ $\newline$ ( $3$ ) $15 t+0.08<3 t+0.12$ $\newline$ ( $4$ ) $15 t+0.08>3 t+0.12$ $\newline$ $5$ . Show work for the following question ( $3$ points) $\newline$ Julia is $4$ years older than twice Kelly's age, $x$ . The product of their ages is $96$ . Write an equation that models this situation. $\newline$ Determine Kelly's age algebraically.

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Write and solve direct variation equations

Full solution

Q. (

23

)

15+0.08 t>3+0.12 t

\newline

(

3

)

15 t+0.08<3 t+0.12

\newline

(

4

)

15 t+0.08>3 t+0.12

\newline

5

. Show work for the following question (

3

points)

\newline

Julia is

4

years older than twice Kelly's age,

x

. The product of their ages is

96

. Write an equation that models this situation.

\newline

Determine Kelly's age algebraically.

Define Kelly's Age: Let Kelly's age be $x$ years. $\newline$ Julia's age is $4$ years older than twice Kelly's age, so Julia's age is $2x + 4$ .
Calculate Julia's Age: The product of their ages is $96$ . So, we write the equation $(2x + 4) \cdot x = 96$ .
Write Product Equation: Distribute $x$ across the terms in the parentheses. $\newline$ $2x^2 + 4x = 96$ .
Simplify Equation: Bring all terms to one side to set the equation to zero. $\newline$ $2x^2 + 4x - 96 = 0$ .
Factor Quadratic Equation: Divide the entire equation by $2$ to simplify. $x^2 + 2x - 48 = 0$ .
Set Factors Equal: Factor the quadratic equation. $\newline$ $(x + 8)(x - 6) = 0$ .
Solve for x: Set each factor equal to zero and solve for x. $\newline$ $x + 8 = 0$ or $x - 6 = 0$ .
Solve for x: Set each factor equal to zero and solve for x. $\newline$ $x + 8 = 0$ or $x - 6 = 0$ .Solve for x. $\newline$ $x = -8$ or $x = 6$ . $\newline$ Since age can't be negative, $x = 6$ is the correct solution.

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