Answer:10 T- shirts were sold
20 hats were sold
20 belts were sold.
Explanation:
Let x represent the number of T shirts that Kelly sold at the flea market.
Let y represent the number of hats that Kelly sold at the flea market.
Let z represent the number of belts that Kelly sold at the flea market.
Kelly sold 50 items at the flea market. This means that
x + y + z = 50 - - - - - - - - - -1
She sold T-shirts for 6$, hats for 8$, and belts for 12$. Her revenue for the day was 460$. This means that
6x + 8y + 12z = 460 - - - - - - - -2
The number of belts sold was twice the difference of the number of hats and the number of T-shirts sold. This means that
z = 2(y - x)
z = 2y - 2x- - - - - - - - -3
Substituting equation 3 into equation 1 and equation 2, it becomes
x + y + 2y - 2x = 50
- x + 3y = 50 - - - - - - - - 4
6x + 8y + 12(2y - 2x) = 460
6x + 8y + 24y - 24x = 460
- 18x + 32y = 460 - - - - - - - - -5
Multiplying equation 4 by 18 and equation 5 by 1, it becomes
- 18x + 54y = 900
- 18x + 32y = 460
Subtracting, it becomes
22y = 440
y = 440/22 = 20
Substituting y = 20 into equation 4, it becomes
- x + 3 × 20 = 50
- x + 60 = 50
- x = 50 - 60 = - 10
x = 10
Substituting x = 10 and y = 20 into equation 1, it becomes
10 + 20 + z = 50
z = 50 - 30 = 20