Ken and Ben were both saving money to buy a TV. Ken was $255 short of the amount needed and Ben was $315 short of the amount needed to buy the TV. If they combined their money, they had eaxctly enough to buy one TV. how much did the TV cost?
If they have enough together to buy a tv, then Ken must be short exactly what Ben has, and vice-versa. So, a tv costs 255+315 = 570.
or, algebraically, since a TV costs as much as they have together,
k = (k+b)-255
b = (k+b)-315
(k,b) = (315,255)
tv = k+b = 570
To find out the cost of the TV, we need to add up the amounts that Ken and Ben were short by.
Let's assume the cost of the TV is x dollars.
According to the problem, Ken was $255 short, so his total savings would be (x - $255) dollars.
Similarly, Ben was $315 short, so his total savings would be (x - $315) dollars.
When they combine their savings, it should equal the cost of the TV, so we can set up the equation:
(x - $255) + (x - $315) = x
Now, let's solve the equation:
2x - $570 = x
Subtract x from both sides:
x - $570 = 0
Add $570 to both sides:
x = $570
Therefore, the cost of the TV is $570.