Two numbers

Numbers A and B differ by 95. If from number A we subtract two thirds of it, we get the same result as when we add three fifths to number B.
Decide for each of the following statements whether it is true (T) or not (N).
a) The larger of the two numbers is even and the smaller of the two numbers is odd.
b) Both obtained results are equal to the number 40.
c) The smaller number is a quarter of the larger number.

Result

a=

Yes

No

b=

Yes

No

c=

Yes

No

Step-by-step explanation:

$$\begin{gathered} A=B+95 \\ A-\frac{2}{3}\cdot A=B+\frac{3}{5}\cdot B \\ A-2/3\cdot A=B+3/5\cdot B \\ A-B=95 \\ 5A-24B=0 \\ Pivot:Row1\leftrightarrow Row2 \\ Row2-\frac{1}{5}\cdot Row1\to Row2 \\ 3.8B=95 \\ B=\frac{95}{3.8}=25 \\ A=\frac{0+24B}{5}=\frac{0+24\cdot 25}{5}=120 \\ A=120 \\ B=25 \\ {x}_1=A/2=120/2=60 \\ {x}_2=B/2=25/2=\frac{25}{2}=12\frac{1}{2}=12.5 \\ a=1 \end{gathered}$$

$b=0$

$c=0$

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