Question

John and Sarah have been married for exactly 37 years. Sarah is four years older than John. In the current year, the sum of their ages is 124. We wish to use this information to determine their ages when they were first married. (a) Set up and write an equation that represents the unknown ages in terms of Sarah's age when they were first married. (The variable in your equation should represent Sarah's age when they were married.) (b) Use your equation to determine how old Sarah was when they were first married. (c) Use your result fron Part (b) to determine how old John was when they were first married.

Answer 1

(a)
`x+33+x+37=124`

(b) 27 years

(c) 23 years

Explanation:

Let x years be Sarah's age when they married.

Sarah is four years older than John, then x - 4 years is John's age when they married.

John and Sarah have been married for exactly 37 years, then after 37 years,

John's age = x - 4 + 37 = x + 33 years

Sarah's age = x + 37 years

In the current year, the sum of their ages is 124, so

(a) The equation that represents the unknown ages in terms of Sarah's age when they were first married is

`x+33+x+37=124`

(b) Solve this equation

`x+33+x+37=124\\ \\2x+70=124\\ \\2x=124-70\\ \\2x=54\\ \\x=27\ years`

(c) John's age is

`x-4=27-4=23\ years`