At a sale on winter clothing, Cody bought two pairs of gloves and four hats for $43.00. Tori bought two pairs of gloves and two hats for $30.00. Find the coordinate pair solution. *Round your answers to the hundredths (2 places past the decimal) with no spaces in the answer.
Let the price of a pair of gloves be $x and the price of a hat be $y.
From the given information, we can set up the following system of equations:
2x + 4y = 43 (equation 1)
2x + 2y = 30 (equation 2)
To solve this system, we can use the method of substitution or elimination. For this example, let's use the method of elimination.
Multiply equation 2 by 2 to make the coefficients of x in both equations the same:
2(2x + 2y) = 2(30)
4x + 4y = 60 (equation 3)
Now, subtract equation 1 from equation 3 to eliminate the y terms:
4x + 4y - (2x + 4y) = 60 - 43
4x + 4y - 2x - 4y = 17
2x = 17
x = 17/2
x = 8.50
Now substitute the value of x back into equation 1 or 2 to solve for y. Let's use equation 1:
2(8.50) + 4y = 43
17 + 4y = 43
4y = 43 - 17
4y = 26
y = 26/4
y = 6.50
So the solution to the system of equations is (8.50, 6.50).