A collection of 36 shirts and 42 jackets contains 842 buttons. A collection of 66 shirts and 77 jackets contains 137 buttons. Each shirt has the same number of buttons, and each jacket has the same number of buttons. How many buttons are there in a Fiona's Fashion shirt, and how many buttons are there in a jacket?

Step-by-step explanation:

Let x represent the number of buttons on shirts and y represent the number of buttons on jackets.

If 36 shirts and 42 jackets contain 842 buttons. This implies:

36x + 42y = 842 (1)

If 66 shirts and 77 jackets contain 137 buttons. This implies:

66x + 77y = 137 (2)

If you take the first equation: 36x + 42y = 842 and isolate the x, then you will have x = (842 - 42y) / 36

If you substitute x into the second equation:

66 ((842-42y) / 36) + 77y = 137

→ 11 (842-42y) / 6 + 77y = 137

→ 11 (842-42y) + 6 (77y) = 137 (6)

→ 9262 - 462y + 462y = 822

→ 9262 = 822 which reveals that the equations do not have a solution

There are 102 shirts. There are 979 buttons in all. There are 119 jackets in all. All to there are 8 buttons in a jacket