SOLUTION: Jon is 6 years older than his wife Liz. In 4 years, twice his age plus 1 will be 3 times Liz's age 3 years ago. How old are they now?

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Question 36480This question is from textbook
: Jon is 6 years older than his wife Liz. In 4 years, twice his age plus 1 will be 3 times Liz's age 3 years ago. How old are they now? This question is from textbook

Answer by rapaljer(4671) About Me  (Show Source):
You can put this solution on YOUR website!
Let x = Liz's present age
x+ 6 = Jon's present age

In 4 years Liz will be x + 4, and John will be x+ 10.
Three years ago, Liz was x - 3

The second sentence is the equation:
In 4 years, twice Jon's age plus 1 will be 3 times Liz's age 3 years ago.
+2+%28x%2B10%29+%2B1+=+3%28x-3%29+
2x+%2B+20+%2B+1+=+3x+-+9+
2x+%2B+21+=+3x+-+9

Subtract 2x from each side and add +9 to each side:
2x-2x+%2B+21+=+3x+-2x+-+9
21+=+x+-+9

21+%2B+9+=+x+-9%2B9+
+30+=+x

Liz is 30.
Jon is 34.

In 6 years Jon will be 40, and twice his age +1 will be 2*40+1 = 81.

Three years ago, Liz was 27, so three times her age three years ago is also 81.
It checks!!

R^2 at SCC