Finding original price of Tea per kg

Question

A reduction of $ 2 per kg enables a man to purchase 2 kg more tea for

$8. Find original price of tea per kg

Attempt

Let price be $x per kg of tea .So let man buys 10 kg of tea .So total cost is 10x.

Now new price is x-2 per kg so man buys 12 kg of tea So total cost is 12(x-2)

So 12(x-2)=8 gives x =32/12. But textbook states answer as x=4. Can someone explain this

Thanks

Answer 1

Hint. Let $x$ be the initial price per kg of tea and $n$ the initial number of kg you could have with $8$ dollars. Then you have $$ nx=8 \tag1 $$ and $$ (n+2)(x-2)=nx \tag2 $$ Expanding $(2)$ gives $$ nx-2n+2x-4=nx $$ or $$ x-n=2 \tag3 $$ then, using $(1)$, we get $$ x-\frac8x=2 \tag4 $$ or

$$ x^2-2x-8=0 \tag5 $$

Can you take it from here?