Question

Two numbers are in ratio 4:7 .if thrice the larger be added to twice the smaller the sum is 59 .find the number.

Answer 1

Answer:

The required numbers are 8 and 14.  

Step-by-step explanation:

Given : Two numbers are in ratio 4:7. if thrice the larger be added to twice the smaller the sum is 59.

To find : The number?

Solution :

Let the ratio be 'x'.

The number became 4x and 7x.

Thrice the larger number i.e. 3(7x)=21x

Twice the smaller number i.e. 2(4x)=8x

According to question,

$21x+8x=59$

$29x=59$

$x=\frac{59}{29}$

$x=2.03$

Approximately, $x=2$

So, The number became 4x=4(2)=8 and 7x=7(2)=14.

Therefore, The required numbers are 8 and 14.

Answer 2

Answer:

The number can be 8 or 14.

Step-by-step explanation:

Let the two numbers be x and y which are in ratio 4: 7  

So,

x/y=4/7 ____________________________________ (1)

If y is the larger number and x is the smaller number then according to the question thrice the larger number i.e. y is added to twice the smaller number to form result 59 i.e. x

Therefore, in equation it is represented as 3y+2x=59______________(2)

Eqn. 1 can be written as  $\frac{7}{4} x=y$

Put    7/4 x=y in Eqn. 2

$\begin{array}{l}{3\left(\frac{7}{4} x\right)+2 x=59} \\ {\frac{21}{4} x+2 x=59} \\ {\frac{21 x+8 x}{4}=59}\end{array}$

29x=59×4   and  x=8.134 or x=8  

Put x = 8 in Eqn. 1

$\frac{7}{4} \times 8=y \quad \\y=14$

Therefore after solving we found out that x = 8 and y = 14