The ratio of Jane's age to her daughter's age is 9:2.
The sum of their ages is 44. How old is Jane?
A. 22
B. 33
C. 35
D. 36
E. 40

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Ответ:

orangeicecream

01.12.2022

Mathematics

(x, y, z) = (0, 0, 3)

Step-by-step explanation:

The augmented matrix for the system is ...

$\left[\begin{array}{cccc}4&1&-2&-6\\2&-3&3&9\\1&-2&0&0\end{array}\right]$

Subtract 4 times the 3rd row from the first row.

$\left[\begin{array}{cccc}0&9&-2&-6\\2&-3&3&9\\1&-2&0&0\end{array}\right]$

Subtract 2 times the 3rd row from the second row.

$\left[\begin{array}{cccc}0&9&-2&-6\\0&1&3&9\\1&-2&0&0\end{array}\right]$

Subtract 9 times the 2nd row from the first row.

$\left[\begin{array}{cccc}0&0&-29&-87\\0&1&3&9\\1&-2&0&0\end{array}\right]$

Now, the first row can be divided by -29 to give ...

$\left[\begin{array}{cccc}0&0&1&3\\0&1&3&9\\1&-2&0&0\end{array}\right]$

You can subtract 3 times this first row from the second row to get ...

$\left[\begin{array}{cccc}0&0&1&3\\0&1&0&0\\1&-2&0&0\end{array}\right]$

And add 2 times the second row to the third to get ...

$\left[\begin{array}{cccc}0&0&1&3\\0&1&0&0\\1&0&0&0\end{array}\right]$

This matrix now tells you (x, y, z) = (0, 0, 3).

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The ratio of Jane's age to her daughter's age is 9:2. The sum of their ages is 44. How old is Jane? A. 22 B. 33 C. 35 D. 36 E. 40