Question

Which shows the correct solution of the equation7D%7B3%7D%20b%20%3D%2050" id="TexFormula1" title="\frac{1}{2} a + \frac{2}{3} b = 50" alt="\frac{1}{2} a + \frac{2}{3} b = 50" align="absmiddle" class="latex-formula">, when b= 30?

Answer 1

Answer: $a=60$

Step-by-step explanation:

You have the following equation:

$\frac{1}{2} a + \frac{2}{3} b = 50$

 In order to find the solution of the given equation when $b=30$, you need to substitute this value of "b" into the equation and then you must solve for  "a".

Applying this procedure, you get that the solution of the equation when  $b=30$ is:

$\frac{1}{2} a + \frac{2}{3} b = 50\\\\\frac{1}{2} a + \frac{2}{3}(30) = 50\\\\\frac{1}{2} a + \frac{60}{3} = 50\\\\\frac{3a+120}{6}=50\\\\3a=(6)(50)-120\\\\a=\frac{180}{3}\\\\a=60$

Answer 2

Answer:

{a:a=60}

Step-by-step explanation:

The given equation is

$\frac{1}{2}a+\frac{2}{3}b=50$

We first multiply through by the Least Common Multiple of 2 and 3, and simplify.

$\implies6\times\frac{1}{2}a+6 \times\frac{2}{3}b=50\times 6$

$\implies3a+2(2b)=300$

$\implies3a+4b=300$

We then make a the subject,so we subtract 4b from both sides of the equation to get

$3a=300-4b$

We then divide through by 3

$\implies\frac{3a}{3}=\frac{300}{3}-\frac{4b}{3}$

$\implies a=100-\frac{4b}{3}$

We substitute b=30 into the simplified equation to get

$a=100-\frac{4(30)}{3}$

$\implies a=100- \frac{120}{3}$

$\implies a={100-40}$

$\implies a=60$

Hence the correct solution of the equation is {a:a=60}