Answer :
Answer:
$84
Firstly, what we must do, is establish a system of equations:
[tex]\frac{2}{3}J = L -90[/tex]
[tex]J + L = 300[/tex]
Due the circumstances, it is decided we will use the method of substitution:
[tex]\frac{2}{3}J = L - 90[/tex]
[tex]\frac{2}{3}J + 90 = L[/tex]
↓
[tex]J + \frac{2}{3}J + 90 = 300[/tex]
Now, we solve the 2-variable equation above:
[tex]J + \frac{2}{3}J + 90 = 300[/tex]
[tex]J + \frac{2}{3}J = 300 - 90[/tex]
[tex]J + \frac{2}{3}J = 210[/tex]
[tex]J(3) + (\frac{2}{3}J)(3) = 210(3)[/tex]
[tex]3J + 2J = 630[/tex]
[tex]5J = 630[/tex]
[tex]J = \frac{630}{5}[/tex]
[tex]\bf~J = 126[/tex]
Now, we must see how much money each one of them had & the price of the jacket:
Now we know that Jim had $126. In other words, $126 is [tex]\frac{3}{3}[/tex] of his money (total money).
So, if Jim has $126, which corresponds to [tex]\frac{3}{3}[/tex] of his money, [tex]\frac{2}{3}[/tex] of his money is:
[tex]\frac{126}{3} = 42[/tex]
[tex]126 * \frac{2}{3} = 42 + 42[/tex]
[tex]\bf~126 * \frac{2}{3} = 84[/tex]
Hope it helped,
BiologiaMagister