Question

1. let k and t be the current ages of siblings katie and thomas. katie is currently twice the age of thomas. in 6 years, katie will be 4 times thomas’s current age. how old are katie and thomas? (a) write a system of equations to describe the situation. (b) find the solution to the system and answer the question.

Explanation:

Step1: Define variables, set first equation

Let $K$ = Katie's current age, $T$ = Thomas's current age.
Katie is twice Thomas's age:
$K = 2T$

Step2: Set second age equation

In 6 years, Katie's age equals 4×Thomas's current age:
$K + 6 = 4T$

Step3: Substitute $K=2T$ into second equation

Replace $K$ with $2T$ to solve for $T$:
$2T + 6 = 4T$

Step4: Solve for $T$

Rearrange and calculate Thomas's age:
$4T - 2T = 6$
$2T = 6$
$T = \frac{6}{2} = 3$

Step5: Solve for $K$

Use $K=2T$ to find Katie's age:
$K = 2 \times 3 = 6$

Answer:

(a) The system of equations is:
$K = 2T$
$K + 6 = 4T$

(b) Katie is currently 6 years old, and Thomas is currently 3 years old.