Acollection 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

let's cover over the formula of the vertex:

y = a(x – h)^2 + k

in this formula, (h,k) are the vertex, always remember that the positive or negative value of the vertex is based on the sign it has.

for example, if the vertex is -3,-6 then both the x and y value would have the positive sign attached to it and if it were a positive x and y value, then a negative sign would be attached to it.

with that being said, for our problem the x value is a positive one so we are looking for a number with a negative sign next to it, in this case the first and second choice.

however, for the first answer choice it isn't quite part of the formula so we know that the answer choice correctly displays the x value.

to confirm, we can see if the -1 fits correctly with the second answer choice, and as mentioned above a negative number will have a positive sign attached to it. so, for our problem we can see that -1 has been changed to +1, so we can confirm that the second answer choice is correct.

hence, our final answer is y=(x - 1)^2 + 1