a pair of skiis in a set of bindingd=s together cost $494. Find the price of each if the skiis cost $10 less than 6 times as much as the bindings?
x = cost of bindings
6x - 10 = cost of skis
x + (6x - 10) = 494
7x - 10 = 494
7x = 504
x = 72
bindings = $72 ( x = 72)
skis = $422 (6x - 10, 6(72)-10 = 422)
One scoop of ice cream has 5 times
To find the price of each item, let's assign variables to unknowns. Let's say the price of the bindings is B dollars, and the price of the skis is S dollars.
According to the given information, we know that the total cost of a pair of skis and bindings is $494. So we can create an equation based on this:
S + B = 494 ---(Equation 1)
The question also states that the skis cost $10 less than 6 times the price of the bindings. Mathematically, this can be represented as:
S = 6B - 10 ---(Equation 2)
Now we have a system of equations (Equation 1 and Equation 2) that we can solve simultaneously to find the values of S and B.
Let's solve the system:
Substitute the value of S from Equation 2 into Equation 1:
(6B - 10) + B = 494
7B - 10 = 494
Move -10 to the other side by adding 10 to both sides:
7B = 494 + 10
7B = 504
Divide both sides by 7:
B = 504 / 7
B = 72
Now substitute the value of B obtained into either Equation 1 or Equation 2 to find the value of S:
S = 6B - 10
S = 6(72) - 10
S = 432 - 10
S = 422
So, the price of the bindings is $72, and the price of the skis is $422.