Jake and his brother have a combined age of 30 years. If Jake is twice as old as his
( 2 mark)
brother, how old is each of them?

Question

Jake and his brother have a combined age of 30 years. If Jake is twice as old as his ( 2 mark) brother, how old is each of them?

UpStudy AI · Accepted Answer

Let's denote Jake's age as $$ J $$ and his brother's age as $$ B $$.

Given:
1. Jake and his brother have a combined age of 30 years: $$ J + B = 30 $$
2. Jake is twice as old as his brother: $$ J = 2B $$

We can solve these equations to find the ages of Jake and his brother.
Solve the system of equations by following steps:
- step0: Solve using the substitution method:
  $$\left\{ \begin{array}{l}J+B=30\J=2B\end{array}ight.$$
- step1: Substitute the value of $$J:$$
  $$2B+B=30$$
- step2: Simplify:
  $$3B=30$$
- step3: Divide both sides:
  $$\frac{3B}{3}=\frac{30}{3}$$
- step4: Divide the numbers:
  $$B=10$$
- step5: Substitute the value of $$B:$$
  $$J=2	imes 10$$
- step6: Calculate:
  $$J=20$$
- step7: Calculate:
  $$\left\{ \begin{array}{l}B=10\J=20\end{array}ight.$$
- step8: Check the solution:
  $$\left\{ \begin{array}{l}B=10\J=20\end{array}ight.$$
- step9: Rewrite:
  $$\left(B,Jight) = \left(10,20ight)$$
The solution to the system of equations is:
$$ B = 10 $$ and $$ J = 20 $$

Therefore, Jake is 20 years old, and his brother is 10 years old.
Jake is 20 years old, and his brother is 10 years old.

Jake and his brother have a combined age of 30 years. If Jake is twice as old as his
( 2 mark)
brother, how old is each of them?

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