By hypothesis, the price of the shoes is represented by x, and the price of the hat is represented by y. "Devin spent a total of $64 dollars for shoes and a hat" can be represented by the equation x + y = 64 "The shoes cost $6 more than the hat" can be represented by the equation x=y+6
We can now create a system: x + y = 64 (1) x = y + 6 (2)
Let's use the value of x from equation 2 and replace in equation (1): x + y = 64 y + 6 + y = 64 2y + 6 = 64 Subtract 6 from each side to have the variables on a side and the numbers on the other: 2y + 6 = 64 2y + 6 - 6 = 64 - 6 2y = 58 Then divide both sides by 2 to have the variable y alone on the first side and its value on the other side: (2y)/2 = 58/2 y = 29
We found the value of y.
Now let's use the value of y in equation (1), in order to find the value of x: x = y + 6 x = 29 + 6 x = 35
We found the value of x.
So the price of the shoes is x = $35 and the price of the hat is y = $29.
You can recheck your answer (very important): x + y = 29 + 35 = 64 (David spent a total of $64 dollars for shoes and a hat) y + 6 = 29 + 6 = 35 = x (The shoes cost $6 more than the hat)
