Answer:
Damien is 74 years old now
Explanation:
Define the variables:
- Let d = age of Damien
- Let k = age of Keyanna
Given information:
- The sum of the ages of Damien and Keyanna is 100 years.
- 10 years ago, Damien's age was 4 times Keyanna's age.
From the given information, create 2 equations:
Equation 1: d + k = 100
Equation 2: d - 10 = 4(k - 10)
Rewrite Equation 1 to make k the subject:
⇒ k = 100 - d
Substitute this into Equation 2 and solve for d:
⇒ d - 10 = 4(100 - d - 10)
⇒ d - 10 = 400 - 4d - 40
⇒ d - 10 = 360 - 4d
⇒ d - 10 + 10 = 360 - 4d + 10
⇒ d = 370 - 4d
⇒ d + 4d = 370 - 4d + 4d
⇒ 5d = 370
⇒ 5d ÷ 5 = 370 ÷ 5
⇒ d = 74
Therefore, Damien is 74 years old now.