HUSBAND & WIFE

Relevant wiki: Systems of Linear Equations Word Problems - Basic

First, let us define our variables using the first statement:

$t=10x+y$ $h=10y+x$ $x<y<10$

Where $t$ and $h$ are the teacher and her husband, respectively, and $x$ and $y$ are integers. Now, we set up an equation to show the second statement: $h-t=\frac{h+t}{11}$

Substitute and solve in terms of $x$ : $10y+x-(10x+y)=\frac{10y+x+10x+y}{11}$ $9y-9x=y+x$ $x=\frac{4}{5}\times y$

There is only one pair $(x,y)$ that satisfies this equation along with the inequality $x<y<10$ : (4,5). Therefore,

$t=10x+y=10(4)+5=\boxed{45}$

Teacher's age = xy = 10x + y Husband's age = yx = 10y + x From statement,10y + x > 10x + y • • • • • (1) Also (10y + x) - (10x + y) =(10y + x + 10x + y) ×1\11 So expand this to get y =5x\4 Next substitute 5x\4 for y in (1) Expand to get 54 > 45 Therefore, teacher's age is the young age that is 45.