Super J-mart will sell 5 large jars and 2 small jars of their jelly for $19. They will also sell 2 large jars and 5 small jars for $16. What is the price of each jar?

Assuming large jars = x, small jars = y

[tex]5x + 2y = 19 \\ 2x + 5y = 16[/tex]

[tex]5x + 2y = 19 \\ 2y = 19 - 5x \\ y = \dfrac{19}{2} - \dfrac{5}{2} x[/tex]

Substitute that into
[tex]2x + 5( \dfrac{19}{2} - \dfrac{5}{2} x) = 16 \\ 2x + \dfrac{95}{2} - \dfrac{25}{2} x = 16 \\10.5x = 31.5 \\ x = 3[/tex]

Substitute x = 3 into
[tex]y = \dfrac{19}{2} - \dfrac{5}{2}( 3 )\\ y = \dfrac{4}{2} \\ y = 2[/tex]

Price for each large jar = $3
Price for each small jar = $2

Hope this helps. - M