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
Question
2 Answer

1. User Answers rejkjavik
Answer:
a=8
b=29
Stepbystep 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
[tex]ab=21[/tex]
we can solve for 'a'
[tex]a=b+21[/tex]
the difference of five times a and two times b is 18
so, we get
[tex]5a2b=18[/tex]
now, we can plug 'a'
[tex]5(b+21)2b=18[/tex]
now, we can solve for b
[tex]5b+1052b=18[/tex]
[tex]3b+105=18[/tex]
[tex]3b=87[/tex]
[tex]b=29[/tex]
now, we can find 'a'
[tex]a=29+21[/tex]
[tex]a=8[/tex]

2. User Answers OrethaWilkison
Answer:
Values of a and b are;
a = 8 and b = 29
Stepbystep 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;
[tex]5(b+21)2b =18[/tex]
Using distributive property; [tex]a\cdot(b+c) = a\cdot b + a\cdot c[/tex]
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