Math Word Equation

Question

Sabrina is 4 years younger than twice her sister's age. The sum of their ages 80. How old is Sabrina's sister? How old is Sabrina?

Answer 1

Let a represent Sabrina.

Let b represent the sister.

Now, write your two equations. Sabrina (a) is (=) four years younger than twice her sister's age (2b - 4)

a=2b - 4

The sum (+) of their ages (a + b) is (=) 80.

a + b = 80

Now, using the second equation solve for a by subtracting b from both sides.

a = 80 - b

Ssubstitute (80 - b) for a in the first equation and solve for b.

80 - b = 2b - 4; Add b to both sides.

80 = 3b - 4; Add 4 to botb sides.

84 = 3b; Divide both sides by 3.

28 = b.

Now, use either equation by plugging in 28 for b and solve for a. We will use the second equation.

a + 28 = 80.; Subtract 28 from both sides.

a = 52.

Remember we said a was Sabrina's age and b was her sister's age. Let's check the math.

a = 2b - 4

52 = 2 (28) - 4

52= 52 ; we are good here.

a + b = 80

52 + 28 = 80

80=80; we are good here as well.

Therefore, Sabrina's age (a) is 52 and her sister's age (b) is 28.