Question

Fiona's Fashion Store is world renowned for its buttoned uniforms. A collection of 36 shirts and 42 jackets contains 842buttons. A collection of 6 shirts and 7 jackets contains 137buttons. 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?

Answer 1

To solve the problem, what you must do is a system of two equations with two Ingonites that describe the problem.
 Let:
 x = number of shirt buttons.
 y = number of buttons on jackets.
 Writing the system:
 36x + 42y = 842
 6x + 7y = 137
 We observe that the system is linearly dependent, therefore, it can not be solved.
 However, the solution is to solve the system of two equations with two unknowns.
In order to solve it, the system must be linearly independent.

Answer 2

Solution:

Let number of buttons in Shirt = x

And Number of buttons in Jackets = y

36 shirts and 42 jackets contains 842 buttons.

And collection of 6 shirts and 7 jackets contains 137 buttons.

Writing it in terms of equations

→ 36 x + 42 y = 842 -------(1)

→ 6 x + 7 y = 137-----(2) × 6

→ 36 x +42 y = 822  ----(3)

As equation (1) and (3) are such that there x and y coefficient are same , but the constant term on one side of equation are different. It means the two equation have no solution.

I.e → $\frac{a_{1}}{a_{2}} =\frac{b_{1}}{b_{2}} \neq \frac{c_{1}}{c_{2}}$

So, the two equation have no solution.

It means we can't find number of buttons in jackets and shirts.