Question

The price of a shirt is 100 dollars. The store manager gives a discount of 50 dollars. A man and his brother brought 4 shirts and then split the cost. What is the numerical expression that represents this situation.

Answer 1

The price of the shirts is p = 100 $/shirt

The two brothers brought n = 4 shirts. This represent:

$T=n\cdot p=4\cdot100=400$

The store manager gives a discount of 50 dollars:

$T_d=T-50=400-50=350$

The two brothers split the total discounted cost between the two:

$c=\frac{T\text{'}}{2}=\frac{350}{2}=175$

Each brother spent 175 dollars.

We can express it (an leave it unsolved) as:

$\frac{n\cdot p}{2}-d=\frac{4\cdot100}{2}-50$

n: number of shirts purchased.

p: price per shirt.

d: discount on the total purchase.

If the discount is per shirt, we have:

$\frac{n\cdot(p-d)}{2}=\frac{4(100-50)}{2}$

If we solve it, we have:

$\frac{n\cdot(p-d)}{2}=\frac{4(100-50)}{2}=\frac{4\cdot50}{2}=2\cdot50=100$