Math Word Problem Challenge From My Son

Question

In a rush day, Katie purchased several packs of pastels for 12$ at a store near her house.

Typically she would go to a discount store that sells the same postels for 50 cents less

per pack, where she would have been ableo to purchase 2 additional packs for the

same cosr.

What price did Katie pay for one pack of pastels? Whtie the equation that represents

this situation and solve that equation to answer the question

Answer 1

Suppose the price is $ x

Then she can purchase 12/x packs at the first store

At a discount store the price is $ (x - 0.50) per pack

So for $ 12 she can purchase 12 / (x-0.50)

So 12/x + 2 = 12 / (x-0.50)

12/x = 12 / (x-0.50) - 2 = (12 - 2x + 1) / (x - 0.50)

So 12 (x-0.50) = x (12-2x+1)

12x - 6 = 12x - 2x² + x

2x²-x-6 = 0

(2x+3) (x-2) = 0

x = 2

So $ 2

Check.

For $ 12 she can buy 6 packs

If price is $ 1.50 she can but 12/1.5 = 8 packs = 6 + 2