Which shows the correct solution of the equation[tex]\frac{1}{2} a + \frac{2}{3} b = 50[/tex], when b= 30?

In order to find the solution of the given equation when [tex]b=30[/tex], 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 [tex]b=30[/tex] is:

[tex]\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[/tex]

kudzordzifrancis kudzordzifrancis · Answer 2 · 2019-08-20T19:59:11+02:00

Answer:

{a:a=60}

Step-by-step explanation:

The given equation is

[tex] \frac{1}{2}a+\frac{2}{3}b=50[/tex]

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

[tex] \implies6\times\frac{1}{2}a+6 \times\frac{2}{3}b=50\times 6[/tex]

[tex] \implies3a+2(2b)=300[/tex]

[tex] \implies3a+4b=300[/tex]

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

[tex]3a=300-4b[/tex]

We then divide through by 3

[tex] \implies\frac{3a}{3}=\frac{300}{3}-\frac{4b}{3} [/tex]

[tex] \implies a=100-\frac{4b}{3} [/tex]

We substitute b=30 into the simplified equation to get

[tex]a=100-\frac{4(30)}{3} [/tex]

[tex] \implies a=100- \frac{120}{3} [/tex]

[tex] \implies a={100-40} [/tex]

[tex]\implies a=60 [/tex]

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