Question

I know the answer i just need the working! please help...​

Answer 1

Answer: the empty basket's mass is 0.28 kg

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Work Shown:

A = mass, in kg, of 1 apple

B = mass, in kg, of 1 empty basket

10A = mass of 10 apples

10A+B = mass of 10 apples and basket = 0.5

35A = mass of 35 apples

35A + B = mass of 35 apples and basket = 1.05

The system of equations we have is

$\begin{cases}10A+B = 0.5\\35A+B = 1.05\end{cases}$

There are a number of ways to solve. As the top left corner of your paper indicates, we can use a matrix to solve. Either using row reduction or matrix inverse math.

We could also use elimination which I find easiest in this case. I'll use that method. Subtract the equations straight down. Note how the B terms become B-B = 0B = 0 which go away. The A terms become 10A-35A = -25A, and the terms on the right hand side become 0.5-1.05 = -0.55

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We're left with the equation

-25A = -0.55

Divide both sides by -25 to isolate A

A = -0.55/(-25)

A = 0.022

The mass of one apple is 0.022 kg

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Use this value of A to find B

10A + B = 0.5

10*0.022 + B = 0.5

0.22 + B = 0.5

B = 0.5 - 0.22

B = 0.28

Or we could use the other equation to solve for B

35A + B = 1.05

35(0.022) + B = 1.05

0.77 + B = 1.05

B = 1.05 - 0.77

B = 0.28

Either way, the empty basket's mass is 0.28 kg