A corner store sells two kinds of baled goods:cakes and pies.A cake costs $13 and a pie cost $6.In one day ,the store sold 9 baked goods for a total of $75 .How many cakes did they sell

Sold X cakes.

Sold Y pies.

Eq1: x + y = 9.
Eq2: 13x + 6y = 75.
Multiply Eq1 by -6 and add the Eqs.

To determine the number of cakes sold, we can set up a system of equations based on the given information.

Let's assume the number of cakes sold is denoted by 'x'. Since each cake costs $13, the total cost of the cakes sold would be 13x.

Similarly, if the store sold a total of 9 baked goods, and 'x' represents the number of cakes sold, then the number of pies sold would be (9 - x).

Since each pie costs $6, the total cost of the pies sold would be 6(9 - x).

According to the given information, the total sales for the day amounts to $75. Therefore, we can set up the equation:

13x + 6(9 - x) = 75

Now let's solve this equation to find the value of 'x'.

13x + 54 - 6x = 75

Combining like terms:

7x + 54 = 75

Subtracting 54 from both sides:

7x = 21

Dividing both sides by 7:

x = 3

Therefore, the store sold 3 cakes.