Olivia ordered 24 cupcakes and a layer of cake. the layer cost $16 and the total cost of the order was $52. what was the price of each cupcake

Your equation is 24x + 16 = 52 where x is the cost of each individual cupcake.

First step is to take away the 16 from each side so that we only have the cupcakes to deal with the overall cost without the cake.

52 - 16 = 36.

Your new equation is 24x = 36

Divide both sides by 24 to isolate the variable x.

x = 36/24 = 1.5 or 1.50

The cost of each cupcake is $1.50.

the direct variation says that:

then the equation is of the form is given by:

            where k is the constant variation.

from the given table:

consider any value of x and m(x)=y

x = 2 and m(x)=y = 3

substitute these value in [1]; we have;

divide both sides by 2 we get;

⇒

check:

put x = -1 and m(x) = -1.5

substitute in the equation:

-1.5 = -1.5                   true

therefore, the function m(x) represents a direct variation

graph of this function as shown below: