Question

The sum of two numbers is 21. Two-thirds of one of the numbers, added to three quarters of the other number gives 15. Find the two numbers

Answer 1

Answer:

9,12

Step-by-step explanation:

they are 9 and 12

2/3*9+3/4*12=15

Answer 2

The required numbers are 9 and 12

     

Given:

The sum of two numbers is 21

Two-thirds of one of the numbers, added to three quarters of the other number gives 15

To find:

The two numbers

Solution:

Let x and y are two numbers  

Given sum of two numbers is 21  

⇒ x+y = 21 -----(1)

Given Two-thirds of one of the numbers, added to three quarters of the other number gives 15

⇒ $\frac{2x}{3} + \frac{3y}{4} = 15$  

⇒ $\frac{8x+9y}{12} = 15$

⇒ 8x + 9y = 180 ---(2)

8 × (1) = 8x+8y = 168 -----(3)

Now do (2) - (3)

⇒ 8x + 9y - 8x - 8y = 180 - 168

⇒  y = 12    

Substitute y = 12 in (1)

⇒ x + 12 = 21  

⇒ x = 9  

Therefore, the required numbers are 9 and 12      

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