The cost of 5 similar 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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To find the cost of each digital camera, we need to divide the total cost of 5 similar cameras and 3 similar video cameras by the total number of digital cameras.
Let's denote the cost of each digital camera as x.
Since each video camera costs 4 times as much as each digital camera, the cost of each video camera would be 4x.
The cost of 5 similar cameras is 5x, and the cost of 3 similar video cameras is 3 times 4x which is 12x.
So, the equation becomes:
5x + 12x = 3213
Combining like terms, we have:
17x = 3213
To find the value of x, we divide both sides of the equation by 17:
x = 3213 / 17 = 189
Therefore, each digital camera costs $189.
To find the cost of a video camera, we can substitute this value back into the equation:
4x = 4 * 189 = 756
So, each video camera costs $756.
Since John buys a digital camera and a video camera, he pays $189 for the digital camera and $756 for the video camera.
Therefore, John pays a total of $189 + $756 = $945.
cost of digital camera --- x
cost of video camera ---- 4x
5x + 3(4x) = 3213
17x = 3213
x = 189
so digital + video
= x + 4x
= 5x
= 945