Question

The difference of two numbers, a and b, is 21. The difference of 5 times a and two times b is 18. What are the values of a and b?

Answer 1

Answer:

The given numbers are a = -8 and b =  - 29

Step-by-step explanation:

The two given numbers are a and b.  (let a >b)

Now, according to question:

a  - b  = 21  ..........  (1)

5a - 2b  = 18   ........... (2)

Multiply equation (1) with 2 and subtract from  equation(2):

5a  - 2b -  2(a-b)  = 18 - 2(21)

or, 5a - 2b  - 2a + 2b  = 18 -  42

or, 3a  =  - 24

or, a  = -24 / 3 = -8

So, a  = -8

now, a - b = 21

⇒ b  =  a - 21  = -8 - 21  = -29

Hence, the given numbers are a = -8 and b =  - 29