Answer:
The price of T-shirts before the sale = 42 euros
The price of scarves before the sale = -77/2 euros
Step-by-step explanation:
The cost of the items Zina buys from the store initially are;
Two scarves and three T-shirts for 49 euros
The reduction in the price of scarves a week later during sales = 1.5 euros
The reduction in the price of T-shirts a week later during sales = 2 euros
The items Zina bought for 40 euros at the reduced price of the sales opportunity are;
Four scarves and five T-shirts for 40 euros
Let 'x' represent the initial price of a scarf and let 'y' represent the initial price of a T-shirt, we have;
2·x + 3·y = 49...(1)
4·(x - 1.5) + 5·(y - 2) = 40...(2)
Expanding equation (2) gives;
4·x - 6 + 5·y - 10 = 40
4·x + 5·y = 40 + 6 + 10 = 56
∴ 4·x + 5·y = 56...(3)
By multiplying equation (1) by 2 and subtracting the result from equation (3), we get;
4·x + 5·y - 2 × (2·x + 3·y) = 56 - 2 × 49 = -63
-y = -42
y = 42
The price of T-shirts before the sale = 42 euros
x = (49 - 3 × 42)/2 = -77/2
x = -77/2
The price of scarves before the sale = -77/2 euros
(However, if the had bought the 4 scarves and 5 T-shirts during sales at 70 euros, we get;
The price of T-shirts before the sale = 12 euros
The price of scarves before the sale = 6.5 euros.
The allowable total price for the reduced 4 scarves and 5 T-shirts is between 66 and about 82 for both initial prices to be +ve)
