Question

two numbers add up to 70 one third of the larger number is 10 more than one seventh of the smaller number find the number​

Answer 1

Larger number = 42 and smaller number = 28

Step-by-step explanation:

Let the larger number = x and

The smaller number = y

To find, the two numbers = ?

According to question,

x + y = 70                  ...........(1)

And,

$\dfrac{x}{3} =\dfrac{y}{7} +10$

⇒ $\dfrac{x}{3} -\dfrac{y}{7}=10$         ..............(2)

Multiplying equation (1) by $\dfrac{1}{7}$ and adding (2), we get

$\dfrac{x}{7} +\dfrac{y}{7}+\dfrac{x}{3} -\dfrac{y}{7} =\dfrac{70}{7} +10$

⇒ $\dfrac{x}{7}+\dfrac{x}{3}=20$

⇒ $\dfrac{10x}{21} =20$

⇒ x = 42

Put x = 42 in equation (1), we get

42 + y = 70    

⇒ y = 70 - 42 = 28

∴ Larger number = 42 and smaller number = 28

Answer 2

Larger number =42

Smaller number=28

Step-by-step explanation:

Let the larger number be x.

and smaller numaber be y.

according to question

$x+y=70-(i)\\\therefore\frac{1}{3}of x=\frac{1}{7}of y+10\\\frac{x}{3}=\frac{y}{7}+10\\\frac{x}{3}-\frac{y}{7}=10-(ii)$

Solving equation (i) and (ii)

Multiply $\frac{1}{7}$ in equation(i) and 1 in equation (i)

$x+y=70- (i)\times\frac{1}{7}\\\frac{x}{3}-\frac{y}{3}=10-(ii)\times1$

$\frac{x}{7}+\frac{y}{7}=\frac{70}{7}\\\frac{x}{3}-\frac{y}{7}=10\\\frac{x}{7}+\frac{y}{7}=10-(iv)\\\frac{x}{3}-\frac{y}{7}=10-(v)$

Adding equation (iv) and (v)

$\frac{x}{7}+\frac{y}{7}+(\frac{x}{3}-\frac{y}{3})=10+10\\\frac{x}{7}+\frac{x}{3}=20\\\\\frac{10x}{21}=20\\x=42$

put $x=42$ in equation (i)

$42+y=70\\y=28$