Mathematics, 21.12.2020 08:10 maithe

*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. Find the numbers.

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Answer from: vinniemccray70

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,

$5x + 4y = 4400\\\\4x + 5y = 4600$

From equation 1,

$5x + 4y = 4400\\\\5x = 4400-4y\\\\x =\dfrac{ 4400-4y}{5}$

Substitute the value of x in equation 2,

$4(\dfrac{4400-4y}{5}) + 5y = 4600\\\\17600-16y + 25y= 4600\times 5\\\\17600 + 9y = 23000\\\\y = \dfrac{5400}{9}\\\\y = 600$

Substitute the value of x in equation 1,

$5x + 4y = 4400\\\\5x + 4(600) = 4400\\\\5x + 2400 = 4400\\\\5x = 4400-2400\\\\5x = 2000\\\\x = \dfrac{2000}{5}\\\\x = 400$

Hence, The first number be x is 400 and the second number be y is 600.

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Answer from: 24nelsoaddh

The numbers are:

$x=400,\:y=600$

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

$\begin{bmatrix}0.05x+0.04y=44\\ 0.04x+0.05y=46\end{bmatrix}$

isolate x for 0.05x + 0.04y = 44

0.05x + 0.04y = 44

Multiply both sides by 100

$0.05x\cdot \:100+0.04y\cdot \:100=44\cdot \:100$

5x+4y=4400

5x=4400-4y

Divide both sides by 5

$\frac{5x}{5}=\frac{4400}{5}-\frac{4y}{5 }$

$x=\frac{4400-4y}{5}$

$\mathrm{Subsititute\:}x=\frac{4400-4y}{5}$

$0.04\cdot \frac{4400-4y}{5}+0.05y=46$

simplify

35.2+0.018y=46

now isolate y for 35.2+0.018y=46

35.2+0.018y=46

$\mathrm{Multiply\:both\:sides\:by\:}1000$

$35.2\cdot \:1000+0.018y\cdot \:1000=46\cdot \:1000$

35200+18y=46000

18y=10800

Divide both sides by 18

$\frac{18y}{18}=\frac{10800}{18}$

y=600

$\mathrm{For\:}x=\frac{4400-4y}{5}$

$\mathrm{Subsititute\:}y=600$

$x=\frac{4400-4\cdot \:600}{5}$

x=400

Therefore, the numbers are:

$x=400,\:y=600$

Answer from: Quest

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step-by-step explanation:

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Answer from: Quest

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step-by-step explanation:

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