Answer:
[tex]a = 2\frac{1}{7}[/tex]
Step-by-step explanation:
Solving for a:
[tex]\frac{5}{3}a + 100 = 200-45a[/tex] (equation given)
[tex]\frac{5}{3}a+45a=200-100[/tex] (minus [tex]100[/tex] and add [tex]45a[/tex] on both sides)
[tex]\frac{140}{3}a = 100[/tex]
[tex]140a = 300[/tex]
[tex]a = \frac{15}{7}[/tex]
[tex]=2\frac{1}{7}[/tex]
Verification:
To verify the answer, we can substitute the number in:
[tex]\frac{5}{3}a+100 = \frac{5}{3}( \frac{15}{7})+100[/tex] (left side of the equation)
[tex]= \frac{725}{7}[/tex]
[tex]200-45a = 200-45(\frac{15}{7})[/tex] (right side of the equation)
[tex]=200-\frac{675}{7}[/tex]
[tex]=\frac{725}{7}[/tex]
Since the left side of the equation = right side of the equation when [tex]\frac{15}{7}[/tex] is substituted in the equation, that means our answer is correct.
∴ [tex]a=2\frac{1}{7}[/tex]
Hope this helps :)
