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Fiona's Fashion Store is world renowned for its buttoned uniforms. A collection of 36 shirts and 42 jackets contains 842 buttons. A collection of 6 shirts and 7 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? Choose 1 answer: (A) There is not enough information to determine the exact number of buttons in a shirt or jacket. (B) The given information describes an impossible situation. (C) There are 10 buttons in a single shirt and 11 buttons in a single jacket. (D) There are 11 buttons in a single shirt and 10 buttons in a single jacket.

Fiona's Fashion Store is world renowned for its buttoned uniforms.\newlineA collection of 3636 shirts and 4242 jackets contains 842842 buttons. A collection of 66 shirts and 77 jackets contains 137137 buttons. Each shirt has the same number of buttons, and each jacket has the same number of buttons.\newlineHow many buttons are there in a Fiona's Fashion shirt, and how many buttons are there in a jacket?\newlineChoose 11 answer:\newline(A) There is not enough information to determine the exact number of buttons in a shirt or jacket.\newline(B) The given information describes an impossible situation.\newline(C) There are 1010 buttons in a single shirt and 1111 buttons in a single jacket.\newline(D) There are 1111 buttons in a single shirt and 1010 buttons in a single jacket.

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Q. Fiona's Fashion Store is world renowned for its buttoned uniforms.\newlineA collection of 3636 shirts and 4242 jackets contains 842842 buttons. A collection of 66 shirts and 77 jackets contains 137137 buttons. Each shirt has the same number of buttons, and each jacket has the same number of buttons.\newlineHow many buttons are there in a Fiona's Fashion shirt, and how many buttons are there in a jacket?\newlineChoose 11 answer:\newline(A) There is not enough information to determine the exact number of buttons in a shirt or jacket.\newline(B) The given information describes an impossible situation.\newline(C) There are 1010 buttons in a single shirt and 1111 buttons in a single jacket.\newline(D) There are 1111 buttons in a single shirt and 1010 buttons in a single jacket.
  1. Equations Setup: Let's denote the number of buttons on a shirt as SS and the number of buttons on a jacket as JJ. We are given two equations based on the collections of shirts and jackets:\newline11) For 3636 shirts and 4242 jackets, the total number of buttons is 842842.\newline22) For 66 shirts and 77 jackets, the total number of buttons is 137137.\newlineWe can write these as two linear equations:\newline36S+42J=84236S + 42J = 842 (Equation 11)\newline6S+7J=1376S + 7J = 137 (Equation 22)
  2. Simplify Equation 22: We can simplify Equation 22 by dividing all terms by the greatest common divisor of the coefficients, which is 11 in this case, so the equation remains the same:\newline6S+7J=1376S + 7J = 137 (Simplified Equation 22)\newlineThis equation can be used to express SS in terms of JJ or vice versa. However, we notice that Equation 22 is a scaled-down version of Equation 11. If we multiply Equation 22 by 66, we should get Equation 11.
  3. Check Equations Relationship: Let's multiply Equation 22 by 66 to see if it matches Equation 11:\newline6×(6S+7J)=6×1376 \times (6S + 7J) = 6 \times 137\newline36S+42J=82236S + 42J = 822\newlineWe immediately see that this does not match Equation 11, which has a total of 842842 buttons. This indicates that the given information describes an impossible situation because the ratios of shirts to jackets and buttons should be consistent.

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