Answer:
x = 45
Step-by-step explanation:
Let the present age of Carl be x.
Given Tina's present age is 15 and 3 years ago, the ratio of Tina's and Carl's ages was 2:7
Then 3 years ago, Tina's age will be
[tex] \\ 15 - 3 = 12 \: years[/tex]
and, Carl's age will be x - 3
and they are in the ratio 2:7.
therefore,
[tex] \\ \: \: \: \: \: \: \: \: 12 \ratio(x - 3) = 2 \ratio7[/tex]
[tex] \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \frac{12}{x - 3} = \frac{2}{7} [/tex]
[tex] \\ \sf \: by \: cross \: multiplication[/tex]
[tex] \\ \: \: \: \: \: \: 12 \times 7 = 2(x - 3) [/tex]
[tex] \\ \: \: \: \: \: \: x - 3 = \frac{84}{2} = 42[/tex]
[tex] \\ \: \: \: \: \: \: \: \: \: \: \: \: x = 42 + 3[/tex]
[tex] \\ \: \: \: \: \: \: \: \: \: \: \: \: \therefore \: \: x = 45[/tex]
