Question

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?

Answer 1

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  $T= \frac{2}{5}J-1$

iii) 

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

means $T= \frac{1}{3}M$

equalize equations ii) and iii):

$\frac{2}{5}J-1= \frac{1}{3}M$        (they are both equal to T)

substitute M=J+2 from equation i:

$\frac{2}{5}J-1= \frac{1}{3}(J+2)$

$\frac{2J-5}{5}= \frac{J+2}{3}$

$3(2J-5)=5(J+2)$

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

so M=25+2=27 (dollars)

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


Answer: 52 $