Question

sylc algebra 1a - standard (15260) modeling with systems of linear equations adele is 5 years older than timothy. in three years, timothy will be \\(\frac{3}{4}\\) of adeles age. what is adeles current age?

Explanation:

Step1: Define variables

Let \( T \) be Timothy's current age and \( A \) be Adele's current age.

Step2: Set up equations

From "Adele is 5 years older than Timothy", we get \( A = T + 5 \).
In three years, Timothy's age will be \( T + 3 \) and Adele's age will be \( A + 3 \). From "In three years, Timothy will be \(\frac{3}{4}\) of Adele's age", we get \( T + 3=\frac{3}{4}(A + 3) \).

Step3: Substitute \( A \) in the second equation

Substitute \( A=T + 5 \) into \( T + 3=\frac{3}{4}(A + 3) \):
\( T + 3=\frac{3}{4}((T + 5)+ 3) \)
Simplify the right - hand side:
\( T + 3=\frac{3}{4}(T + 8) \)
Multiply both sides by 4 to get rid of the fraction:
\( 4(T + 3)=3(T + 8) \)
Expand both sides:
\( 4T+12 = 3T + 24 \)
Subtract \( 3T \) from both sides:
\( 4T-3T+12=3T - 3T+24 \)
\( T + 12=24 \)
Subtract 12 from both sides:
\( T=24 - 12=12 \)

Step4: Find Adele's current age

Since \( A=T + 5 \) and \( T = 12 \), then \( A=12 + 5=17 \).

Answer:

Adele's current age is 17.