Answer:
a = 1, b = 4
Step-by-step explanation:
You have worked out part (a) correctly, that is
0.7575... = [tex]\frac{75}{99}[/tex] = [tex]\frac{25}{33}[/tex]
(b)
[tex]\frac{a}{11}[/tex] + [tex]\frac{b}{6}[/tex] = [tex]\frac{25}{33}[/tex]
[tex]\frac{6a+11b}{66}[/tex] = [tex]\frac{25}{33}[/tex]
Multiply numerator/ denominator of [tex]\frac{25}{33}[/tex] by 2, thus
[tex]\frac{25(2)}{33(2)}[/tex] = [tex]\frac{50}{66}[/tex] , then
[tex]\frac{6a+11b}{66}[/tex] = [tex]\frac{50}{66}[/tex] , thus
6a + 11b = 50
Choose a = 1 ( a positive integer ), then
6(1) + 11b = 50
6 + 11b = 50 ( subtract 6 from both sides )
11b = 44 ( divide both sides by 11 )
b = 4
a = 1, b = 4, so
[tex]\frac{1}{11}[/tex] + [tex]\frac{4}{6}[/tex] = [tex]\frac{25}{33\\}[/tex]
