We are buying a total of 12 fruits (apples and bananas) for 132 dollars. If the apples are 3 dollars more expensive than the bananas, and we bought more apples than bananas, how many bananas we bought?
Or in other words:
- Let $a=$ Apple price
- Let $b=$ Banana price
- Let $x=$ Apples bought
- Let $y=$ Bananas bought
We know that:
$$x+y=12$$
$$x>y$$
$$a=b+3$$
$$xa+yb=132$$
therefore $$x(b+3) + yb=132$$
which yields $x=44-4b$ or $y=4b-32$
Let be $\,x=$ the number of apples, $\,a=$ price of each apple, $\,y=$number of bananas, $\,b=$ price of each banana, then you have the equations
$$x+y=12\Longleftrightarrow x = 12-y\;\;,\;\;\;ax+by=132\;\;,\;\;\;a=b+3\Longleftrightarrow$$
$$(b+3)(12-y)+by=132\Longleftrightarrow 4b-y=32$$
Do a little more algebra, take into account that $\,y>x\,$ and they both are integers...and what is a clear divisor of $\,y\,$?