Kelly sold 50 items at a flea market. she sold t-shirts for 6$, hats for 8$, and belts for 12$. her revenue for the day was 460$. the number of belts sold was twice the difference of the number of hats and the number of t-shirts sold. how many hats were sold?

10 T- shirts were sold

20 hats were sold

20 belts were sold.

Step-by-step 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