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 information given, we can set up the following system of equations:
2x + 4y = 43 (equation 1)
2x + 2y = 30 (equation 2)
We can solve this system of equations to find the values of x and y.
Multiply equation 2 by -2 to eliminate the x term:
-4x - 4y = -60
Add this to equation 1:
2x + 4y = 43
-4x - 4y = -60
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-2x = -17
Divide both sides by -2:
x = 8.50
Substitute this value back into equation 2 to find y:
2(8.50) + 2y = 30
17 + 2y = 30
2y = 13
y = 6.50
Therefore, the coordinate pair solution is (8.50, 6.50).