The cost of 5 similar digital cameras and 3 similar video cameras is $3,213. 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?
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Let's start by assigning variables to the cost of the digital camera and the video camera.
Let's say the cost of each digital camera is represented by 'x' dollars.
Since each video camera costs 4 times as much as each digital camera, the cost of each video camera would be 4 * x = '4x' dollars.
Now, let's use this information to set up an equation to find the cost of each camera:
5x (cost of 5 digital cameras) + 3(4x) (cost of 3 video cameras) = $3,213.
Simplifying the equation, we have:
5x + 12x = $3,213.
17x = $3,213.
Now, to find the cost of 1 digital camera, we divide both sides of the equation by 17:
x = $3,213 / 17.
x ≈ $189.
Therefore, the cost of 1 digital camera is approximately $189.
And the cost of 1 video camera is 4 * x = 4 * $189 = $756.
To find out how much John pays for a digital camera and a video camera, we add the cost of each camera:
$189 (digital camera) + $756 (video camera) = $945.
So, John pays $945 for a digital camera and a video camera.
To find the cost of each camera, we can set up a system of equations.
Let's assume the cost of each digital camera is x dollars. Therefore, the cost of each video camera would be 4x dollars.
According to the information given, the cost of 5 similar digital cameras and 3 similar video cameras is $3,213.
So, we can write the equation as follows:
5x + 3(4x) = $3,213
Simplifying the equation:
5x + 12x = $3,213
17x = $3,213
x = $3,213 / 17
x ≈ $189
Therefore, the cost of each digital camera is approximately $189, and the cost of each video camera is 4 times that, which is approximately $756.
Since John buys one digital camera and one video camera, he pays $189 + $756 = $945.