Question

The sum of a number and 3 times a second number is represented by a+3b=39. The sum of half of the first number and 1/3 of the second number is represented by 12a+13b=9.
What is the first number (a)?
a =
What is the second number (b)?
b =
Please I need help I keep getting something unreasonable

Answer 1

You can set the first equation by a, that would be
a = 39 - 3b
then you plug in 39 - 3b into 'a' on the next equation
1/2(39 - 3b) + 1/3b = 9
simplify it
19.5 - 1.5b + 1/3b = 9
-10.5 = -7/6b
b = 9
plug in 9 in the first equation
a + 3 (9) = 39
a = 39 - 27
a = 12

FINAL
a = 12
b = 9

Answer 2

Answer:  The first number is a = 12 and the second number is b = 9.

Step-by-step explanation:  Given that the first number a and second number b is related to each other by the following system of equations :

$a+3b=39~~~~~~~~~~~~~~~~~~~~~~~(i)\\\\\\\dfrac{1}{2}a+\dfrac{1}{3}b=9~~~~~~~~~~~~~~~~~~~~~~(ii)$

We are to find the first and second number, i.e., a and b.

From equation (i), we have

$a+3b=39\\\\\Rightarrow a=39-3b~~~~~~~~~~~~~~~~~~~~~`(iii)$

Substituting the value of a from equation (iii) in equation (ii), we get

$\dfrac{1}{2}\times(39-3b)+\dfrac{1}{3}b=9\\\\\\\Rightarrow \dfrac{3(39-3b)+2b}{6}=9\\\\\Rightarrow 117-9b+2b=9\times6\\\\\Rightarrow 117-7b=54\\\\\Rightarrow 7b=117-54\\\\\Rightarrow 7b=63\\\\\Rightarrow b=\dfrac{63}{7}\\\\\Rightarrow b=9.$

Putting the value of b in equation (iii) we get

$a=39-3\times9=39-27=12.$

Thus, the first number is a = 12 and the second number is b = 9.