the cost of 5 digital cameras and 3 similar video cameras is 3213.00. each video camera costs 4 times as much as each digital camera. john buys a digital camera and a video camera. how much does he pay?

digital camera --- x

video camera ---- 4x

5x + 3(4x) = 3213

solve for x

Let's represent the cost of a digital camera as 'x' and the cost of a video camera as 'y'.

Given that 5 digital cameras and 3 video cameras cost $3213, we can set up the following equations:

5x + 3y = 3213 ...(i) (Cost of 5 digital cameras and 3 video cameras is $3213)
y = 4x ...(ii) (Each video camera costs 4 times as much as each digital camera)

To find the value of 'x', we substitute equation (ii) into equation (i):

5x + 3(4x) = 3213
5x + 12x = 3213
17x = 3213
x = 3213 / 17
x = 189

We have found that the cost of a digital camera is $189.

Now, to find the cost of a video camera (y), we substitute the value of 'x' into equation (ii):

y = 4(189)
y = 756

We have found that the cost of a video camera is $756.

So, John pays the cost of a digital camera ($189) plus the cost of a video camera ($756):

John pays $189 + $756 = $945.

To find the cost of the digital cameras and video cameras, we can set up a system of equations based on the given information.

Let's use the variable "x" to represent the cost of each digital camera and "y" to represent the cost of each video camera.

From the information given, we are given two equations:

1) 5x + 3y = 3213 (the cost of 5 digital cameras and 3 video cameras is $3213)

2) y = 4x (each video camera costs 4 times as much as each digital camera)

To solve this system of equations, we can substitute equation 2) into equation 1) to eliminate the variable "y":

5x + 3(4x) = 3213

Simplifying the equation:

5x + 12x = 3213

17x = 3213

Divide both sides of the equation by 17:

x = 189

Now that we know the cost of each digital camera (x = $189), we can substitute this value back into equation 2) to find the cost of each video camera:

y = 4(189)

y = 756

Therefore, each digital camera costs $189 and each video camera costs $756.

Finally, to find out how much John pays for one digital camera and one video camera, we just add their prices:

189 + 756 = $945.

Therefore, John pays $945 for one digital camera and one video camera.