Question

Two numbers are in the ratio 4:7 . If thrice the larger be added to twice the smaller , the sum is 59 .find the numbers .( form the pair of linear equations for this problem and find their solution by substitution method)

Answer 1

Answer:

14 and 8

Step-by-step explanation:

Given:

• Two numbers are in the ratio of 4:7

• If thrice the larger be added to twice the smaller , then the sum is equal to 59

To find:

• Forming pair of linear equations and finding solution by substitution method

Let the first number be 4x

Then the second number is equal to 7x

According to the question,

3(7x)+2(4x)=59

21x+8x=59

29x=59

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

X=2.03

X≈2

First number ≈ 4x = 4×2=8

Second number ≈ 7x = 7×2=14

The larger number and smaller numbers are 14 and 8 approximately

Answer 2

Answer:

Given:

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

Find:

• Find the numbers (form the pair of linear equations for this problem and find their solution by substitution method).

Note:

• According to the question let us assume, x as number, 4x as the first number and 7x be the second number.

Calculations:

⇢ $\sf{3 \times 7x + 2 \times 4x = 59}$

⇢ $\sf{21x + 8x = 59}$

⇢ $\sf{29x = 59}$

⇢ $\sf{x = {\dfrac{59}{29}}}$

⇢ $\sf{x=2.03}$

⇢ $\bold{x = 2}$

⇢ $\sf{4x = 4 (2) =8}$

⇢ $\sf{7x = 7(2)=14}$

Therefore, the required numbers are 8 and 14.