Question

14. 0.5x + 0.7y = 0.74
0.3x + 0.5y = 0.5​

Answer 1

$\Large{\textbf{\underline{\underline{According\;to\;the\;Question}}}}$

Given,

0.5x + 0.7y = 0.74 …………...(1)

0.3x - 0.5y = 0.5 …………......(2)

Now,

Multiply (1) and (2) by 100,

50x + 70y = 74 ……….... (3)

30x + 50y = 50 ………... (4)

Now,

From (3) we have,

50x = 74 - 70y

x = (74 - 70y)/50 …………(5)

Here,

Putting value of x in (4),

30x + 50y = 50

30 (74 - 70y)/50 + 50y = 50

3(74 - 70y)/5 + 50y = 50

[(222 - 210y) + 250y]/5 = 50

[222 - 210y + 250y] = 50 × 5

40y = 250 - 222

40y = 28

y = 28/40

y = 7/10

y = 0.7

Now,

Substituting value of y in (5),

x = (74 - 70y)/50

x = (74 - 70 × 0.7)/50

x = (74 - 49)/50

x = 25/50

x = 5/10

x = 0.5

Therefore,

x = 0.5 and y = 0.7

Answer 2

Subject:

Math

To Find:

X and Y.

Solutions:

$\displaystyle \mathsf{\:\left(\frac{1}{2}\right)x+\left(\frac{7}{10}\right)y=\left(\frac{37}{50}\right)}}$

First, subtract by (7/10)y from both sides of an equation.

$\displaystyle \mathsf{\frac{1}{2}x+\frac{7}{10}y-\frac{7}{10}y=\frac{37}{50}-\frac{7}{10}y}}$

Solve.

$\displaystyle\mathsf{\frac{1}{2}x=\frac{37}{50}-\frac{7}{10}y}}$

Multiply by 2 from both sides of an equation.

$\displaystyle \mathsf{2\cdot \frac{1}{2}x=2\cdot \frac{37}{50}-2\cdot \frac{7}{10}y}}}$

Solve.

$\displaystyle \mathsf{x=\frac{37}{25}-\frac{7}{5}y}}$

Solve (isolate by the y).

$\displaystyle \mathsf{\frac{3}{10}\left(\frac{37}{25}-\frac{7}{5}y\right)+\frac{1}{2}y=\frac{1}{2}}}$

$\displaystyle \mathsf{X=\frac{37}{25}-\frac{7}{5}y, y= \frac{7}{10} }}$

Rewrite the problem down.

$\displaystyle \mathsf{x=\frac{37}{25}-\frac{7}{5}\cdot \frac{7}{10}}}$

Solve.

$\displaystyle \mathsf{\frac{37}{25}-\frac{7}{5}\cdot \frac{7}{10}=\frac{1}{2}}}}}}}}$

$\displaystyle \mathsf{x=\frac{1}{2} }}}$

$\displaystyle \mathsf{y=\frac{7}{10} }}$

Divide by both fractions as a decimal.

$\displaystyle \mathsf{\frac{1}{2}=0.5 }}}\\\\\\\displaystyle \mathsf{\frac{7}{10}=0.7 }}}\\\\\\\displaystyle \mathsf{\boxed{\mathsf{x=0.5, \quad y=0.7}}}}$

Answers:

Therefore, the correct answer is x=0.5, and y=0.7.