Question

sam and harry are family. sam is currently three times harrys age. sams age is also 10 more than twice harrys age. the following system of equations models this scenario:
x = 3y
x = 10 + 2y
what are their current ages?
○ sam is 24 years old, and harry is 8 years old.
○ sam is 39 years old, and harry is 13 years old.
○ sam is 27 years old, and harry is 9 years old.
○ sam is 30 years old, and harry is 10 years old.

Explanation:

Step1: Set equations equal

Since \( x = 3y \) and \( x = 10 + 2y \), substitute \( x \) from first into second: \( 3y = 10 + 2y \)

Step2: Solve for y

Subtract \( 2y \) from both sides: \( 3y - 2y = 10 + 2y - 2y \) → \( y = 10 \)

Step3: Find x

Substitute \( y = 10 \) into \( x = 3y \): \( x = 3\times10 = 30 \)

Answer:

Sam is 30 years old, and Harry is 10 years old.