Question

the diffrence of two numbers,a and b,is 21,the diffrence of five times a and two times b is 18 what are the values of a and b

Answer 1

Answer:

a=-8

b=-29

Step-by-step explanation:

Let's assume

first number is a

second number is b

the difference of two numbers,a and b,is 21

so, we get

$a-b=21$

we can solve for 'a'

$a=b+21$

the difference of five times a and two times b is 18

so, we get

$5a-2b=18$

now, we can plug 'a'

$5(b+21)-2b=18$

now, we can solve for b

$5b+105-2b=18$

$3b+105=18$

$3b=-87$

$b=-29$

now, we can find 'a'

$a=-29+21$

$a=-8$

Answer 2

Answer:

Values of a and b are;

a = -8 and b  = -29

Step-by-step explanation:

As per the statement:

Difference of two numbers, a and b is 21

i.e,  a -b = 21                      .......[1]

Also, it is given that the difference of five times a and two times b is 18.

"five times a" means 5a

"two times b" means 2b

then;

5a - 2b = 18                        ......[2]

We can write equation [1] as;

a = b + 21                           .....[3]

Substitute the value of a in equation [2] we have;

$5(b+21)-2b =18$

Using distributive property;  $a\cdot(b+c) = a\cdot b + a\cdot c$

5b + 105 - 2b = 18

combine like terms we get;

3b = 18 -105

Simplify:

3b = -87

Divide by 3 on both sides we get;

b = -29

Substitute the value of b in equation [3] to solve for a;

a = -29 + 21 = -8

Therefore, the values of a and b is, -8 and -29