Joe and mary each pay the same price for a t-shirt. before they buy it, mary has $\$ 2$ more than joe. to buy the t-shirt, joe spends $ \$1 $ less than $\frac{2}{5}$ of his money, and mary spends $\frac{1}{3}$ of her money. what was the total amount of money joe and mary originally had altogether?

Let Joe initially have J dollars, and Mary have M dollars. Let the price of the T-shirt be T dollars.

i) "Before they buy it, Mary has 2$ more than Joe":

means M=J+2

ii)

"To buy the T-shirt, Joe spends 1 $ less than \frac{2}{5} of his money"

so  

iii) 

"Mary spends \frac{1}{3} of her money"

means 

equalize equations ii) and iii):

       (they are both equal to T)

substitute M=J+2 from equation i:







6J-15=5J+10
J=25

so M=25+2=27 (dollars)

Together Mary and Joe had 27+25=52 (dollars)

52 $