A company sells tshirts sweatshirts and hats In 2014 they so

A company sells t-shirts, sweatshirts, and hats. In 2014, they sold a total of 7,000 t-shirts and hats. In 2015, they sold twice as many hats and three times as many sweatshirts as they had sold in 2014, but sold the same number of t-shirts. In 2015, they sold 1,000 more hats than sweatshirts and a total of 12,000 of all three items. How many t-shirts, sweatshirts, and hats did they sell in 2015?

Solution

for 2014

let T-shirts be represented by = TS

and hats by = H

and sweatshirts = SS

In 2014, they sold a total of 7,000 t-shirts and hats

=> TS + H = 7000   ---------(1)

let SS number of sweatshirts be sold in 2014

In 2015, they sold twice as many hats and three times as many sweatshirts as they had sold in 2014, but sold the same number of t-shirts

=> 2H + 3SS

and TS be the units sold in 2015

In 2015, they sold 1,000 more hats than sweatshirts and a total of 12,000 of all three items

2H = 1000 + 3SS       ----------(2)

and 2H + 3SS + TS = 12000        ----------(3)

now the t shirts sold in 2014 are TS = (7000 - H)    -----------(4)

and we know that the units of t shirts sold in both the years is the same

=> from (3) and (4)

=> 2H + 3SS + 7000 - H = 12000    

H + 3SS = 5000           -------------(5)

from (2) and (5)

2H = 1000 + 3SS

H + 3SS = 5000

=> H = 2000 and SS = 1000

ans we know that

TS = (7000 - H)   => TS = 7000 - 2000 = 5000

hence in 2015

t shirts sold = TS = 5000

hats sold = 2H = 2*2000 = 4000

and sweat shirts sold = 3SS = 3*1000 = 3000