Respuesta :
Answer:
The numbers are:
[tex]x=400,\:y=600[/tex]
Step-by-step explanation:
Let 'x' be the first number
Let 'y' be the first number
5% of x = 5/100x = 0.05x
4% of y = 4/100y = 0.04y
- As the sum of 5% of one number and 4% of a second number is 44.
so the equation becomes
0.05x + 0.04y = 44
Also
4% of x = 4/100x = 0.04x
5% of y = 5/100y = 0.05y
- As the sum of 4% of one number and 5% of a second number is 46.
so the equation becomes
0.04x + 0.05y = 46
Thus, the system of the equations becomes
0.05x + 0.04y = 44
0.04x + 0.05y = 46
solving the system of the equation
[tex]\begin{bmatrix}0.05x+0.04y=44\\ 0.04x+0.05y=46\end{bmatrix}[/tex]
isolate x for 0.05x + 0.04y = 44
[tex]0.05x + 0.04y = 44[/tex]
Multiply both sides by 100
[tex]0.05x\cdot \:100+0.04y\cdot \:100=44\cdot \:100[/tex]
[tex]5x+4y=4400[/tex]
[tex]5x=4400-4y[/tex]
Divide both sides by 5
[tex]\frac{5x}{5}=\frac{4400}{5}-\frac{4y}{5 }[/tex]
[tex]x=\frac{4400-4y}{5}[/tex]
[tex]\mathrm{Subsititute\:}x=\frac{4400-4y}{5}[/tex]
[tex]0.04\cdot \frac{4400-4y}{5}+0.05y=46[/tex]
simplify
[tex]35.2+0.018y=46[/tex]
now isolate y for [tex]35.2+0.018y=46[/tex]
[tex]35.2+0.018y=46[/tex]
[tex]\mathrm{Multiply\:both\:sides\:by\:}1000[/tex]
[tex]35.2\cdot \:1000+0.018y\cdot \:1000=46\cdot \:1000[/tex]
[tex]35200+18y=46000[/tex]
[tex]18y=10800[/tex]
Divide both sides by 18
[tex]\frac{18y}{18}=\frac{10800}{18}[/tex]
[tex]y=600[/tex]
[tex]\mathrm{For\:}x=\frac{4400-4y}{5}[/tex]
[tex]\mathrm{Subsititute\:}y=600[/tex]
[tex]x=\frac{4400-4\cdot \:600}{5}[/tex]
[tex]x=400[/tex]
Therefore, the numbers are:
[tex]x=400,\:y=600[/tex]
The first number be x is 400 and the second number be y is 600.
Given that,
The sum of 5% of one number and 4% of a second number is 44.
The sum of 4% of the first number and 5% of the second number is 46.
We have to find,
The numbers.
According to the question,
Let, the first number be x,
And the second number be y,
Then,
5% of x = 0.05x
4% of y = 0.04y
The sum of 5% of one number and 4% of a second number is 44 then, the equation is,
0.05x + 0.04y = 44
And As the sum of 4% of one number and 5% of a second number is 46 then, the equation becomes,
5% of y = 0.05y
4% of x = 0.04x
0.04x + 0.05y = 46
On solving both the equations multiply both the equation by 100,
[tex]5x + 4y = 4400\\\\4x + 5y = 4600[/tex]
From equation 1,
[tex]5x + 4y = 4400\\\\5x = 4400-4y\\\\x =\dfrac{ 4400-4y}{5}[/tex]
Substitute the value of x in equation 2,
[tex]4(\dfrac{4400-4y}{5}) + 5y = 4600\\\\17600-16y + 25y= 4600\times 5\\\\17600 + 9y = 23000\\\\y = \dfrac{5400}{9}\\\\y = 600[/tex]
Substitute the value of x in equation 1,
[tex]5x + 4y = 4400\\\\5x + 4(600) = 4400\\\\5x + 2400 = 4400\\\\5x = 4400-2400\\\\5x = 2000\\\\x = \dfrac{2000}{5}\\\\x = 400[/tex]
Hence, The first number be x is 400 and the second number be y is 600.
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