Question

A's age exceeds twice B's age by 18 years. In 3 years time,
one-third of A's age will exceed B's age by 2 years.
their present ages.​

Answer 1

Their present ages are: A's age is 30 years and B's age is 6 years

Step-by-step explanation:

The given is:

• A's age exceeds twice B's age by 18 years
• In 3 years,  one-third of A's age will exceed B's age by 2 years

The missing question is what are their present ages?

Assume that A's age is x years

∵ B's age = x years

∵ A's age exceeds twice B's age by 18

- That mean A's age is equal to 2 times x plus 18

∴ A's age =  2 x + 18

In three years means add each age by 3

A's age = (2 x + 18) + 3 = 2 x + 18 + 3 = 2 x + 21

B's age = x + 3

∵ In three years A's age = 2 x + 21

∵ In three years B's age = x + 3

∵ One-third of A's age will exceed B's age by 2 years

- That mean multiply A's age by one-third and equate it by B's

  age plus 2

∴ $\frac{1}{3}$ (2 x + 21) = (x + 3) + 2

- Simplify the equation

∴ $\frac{2}{3}$ x + 7 = x + 5

- Subtract 7 from both sides

∴ $\frac{2}{3}$ x = x - 2

- Subtract x from both sides

∴ $-\frac{1}{3}$ x = -2

- Divide both sides by $-\frac{1}{3}$

∴ x = 6

∵ The present B's age is x

∴ The present B's age is 6 years

∵ The present A's age is 2 x + 18

- substitute x by 6

∴ The present A's age = 2(6) + 18 = 12 + 18 = 30 years

Their present ages are: A's age is 30 years and B's age is 6 years

Learn more:

You can learn more about the linear equation in brainly.com/question/3965451

#LearnwithBrainly