A shop sells fruit in two types of gift boxes: standard and deluxe. Each standard box contained 1kg of peaches and 2kg of apples and each deluxe box contains 2kg of peaches and 1.5 kg of apples. On one particular day the shop sold 12kg of peaches and 14kg of apples in gift boxes. How many containers of each kind of box were sold on the day?

Let's call the number of standard boxes sold x and the number of deluxe boxes sold y.
The kg of peaches sold will be 1 for each standard box and 2 for each deluxe, so we know:
x + 2y = 12
The kg of apples sold will be 2 for each standard box and 1.5 for each deluxe, so:
2x + 1.5y = 14. Now we solve the two equations as a system:
From the 1st one:
x = 12 - 2y
We substitute in the second one:
2(12 - 2y) +1.5y = 14;
24 - 4y +1.5y = 14;
-2.5y = -10;
y = 10/2.5 = 4;
Now we substitute in the first equation:
x = 12 - 2y = 12 - 2*4 = 12 - 8 = 4.
So the shop sold 4 standard boxes (x) and 4 deluxe boxes (y).