a coat,shirt and tie cost $300. coat costs twice as much as the shirt. shirt cost $40 more than twice the cost of the tie. what are the cost of each item?
300-40=260
Let x = tie cost, then shirt = 2x+40 and coat = 2(2x+40).
x + (2x+40) + 2(2x+40) = 300
Get rid of parentheses and combine like terms.
x + 2x + 40 + 4x + 80 = 300
7x = 300-120 = 180
Divide by 7.
x = 25.71
From there, calculate the shirt and coat.
To find the cost of each item, let's assign variables to represent the unknowns. Let's call the cost of the tie 'x', the cost of the shirt 'y', and the cost of the coat 'z'.
According to the given information, the coat costs twice as much as the shirt. Therefore, we can write the equation: z = 2y.
We also know that the shirt costs $40 more than twice the cost of the tie. This can be expressed as: y = 2x + $40.
Finally, we are given that the total cost of the coat, shirt, and tie is $300. We can write it as: x + y + z = $300.
Now we have a system of equations to solve:
z = 2y (Equation 1)
y = 2x + $40 (Equation 2)
x + y + z = $300 (Equation 3)
To solve this system of equations, we can use substitution or elimination method. Let's use the substitution method:
From Equation 1, we can substitute 2y in place of z in Equation 3:
x + y + 2y = $300
Simplifying:
x + 3y = $300 (Equation 4)
Now, from Equation 2, we can substitute 2x + $40 in place of y in Equation 4:
x + 3(2x + $40) = $300
Simplifying:
x + 6x + $120 = $300
7x = $300 - $120
7x = $180
x = $180 / 7
x ≈ $25.71
Now we can substitute the value of x back into Equation 2 to find y:
y = 2x + $40
y = 2($25.71) + $40
y = $51.42 + $40
y ≈ $91.42
Finally, we can substitute the values of x and y into Equation 1 to find z:
z = 2y
z = 2($91.42)
z = $182.84
So, the cost of the tie is approximately $25.71, the cost of the shirt is approximately $91.42, and the cost of the coat is approximately $182.84.