# Sue is 7 years older than Bob. Three less than twice Bob's is Sue age, find bob and Sue's ages now?

Sep 21, 2017

Bob is $10$, Sue is $17$.

#### Explanation:

Let Sue $= S$ and Bob $= B$

$S = 2 B - 3$

$S = B + 7$

Since $S = S$, then

$2 B - 3 = B + 7$

Do some algebra to figure out that

$2 B - B = 7 + 3$

$B = 10$

Since Sue is $7$ years older than Bob, she is $17$.

Sep 21, 2017

Bob is 10 Sue is 17

#### Explanation:

Let s = Sue's age
Let b = Bob's age

Sue is 7 years older than Bob so Sue is:

$s = b + 7$ $\left[1\right]$

Three less than twice Bob's age:

$s = 2 b - 3$ $\left[2\right]$

You need to solve these simultaneously.

Substitute for $s$ in equation [ 1 ]

$2 b - 3 = b + 7$

$2 b = b + 10$
$b = 10$
$s = 10 + 7 = 17$