The cost of 5 similar digital cameras and 3 similar video cameras is $3213. 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?
5 x + 3 y = 3213
y = 4 x
5 x + 12 x = 3213
17 x = 3213
x = 189 for digital
4 x = 756 for video
sum = 945
To find out how much John pays for a digital camera and a video camera, we need to follow the given information and perform some calculations.
Let's assign variables to the unknowns:
Let the cost of a digital camera be 'x'.
Each video camera costs 4 times as much as each digital camera, so the cost of a video camera would be 4 * 'x', which is 4x.
According to the given information, the cost of 5 similar digital cameras is $3213, which means:
5 * 'x' = $3213
Dividing both sides of the equation by 5, we find:
'x' = $3213 / 5
'x' = $642.60
So, the cost of a digital camera is $642.60.
To find the cost of a video camera, we can substitute this value of 'x' into our equation:
4x = 4 * $642.60
4x = $2570.40
Therefore, the cost of a video camera is $2570.40.
To find how much John pays for a digital camera and a video camera, we simply add the costs together:
John pays $642.60 (for a digital camera) + $2570.40 (for a video camera) = $3213.00
Thus, John pays $3213.00 for a digital camera and a video camera in total.