Answer:
Sydney is 44 years old.
Explanation:
State your variables
let x be Devaughn's age
let y be Sydney's age
Write equations using information from the problem
x = y - 6 "Devaughn is 6 years younger than Sydney"
x + y = 82 "The sum of their ages is 82"
Solve using the substitution method
Notice that the first equation equals to "x". The second equation has the letter "x". You can replace the second "x" using the expression in the first equation.
x + y = 82 Second equation. Replace "x" with y - 6.
y - 6 + y = 82 Combine like terms (add the "y"s together)
2y - 6 = 82
Start isolating "y"
2y - 6 + 6 = 82 + 6 Add 6 to both sides
2y = 88
2y/2 = 88/2 Divide both sides by 2
y = 44 Sydney's age
Therefore Sydney is 44 years old.
If you needed Devaughn's age:
Substitute y = 44 in the first equation.
x = y - 6
x = 44 - 6 Subtract
x = 38 Devaughn's age