Question

If I give my sister 5 dollars, then we will have the same amount of money. If instead she

gives me 8 dollars, then I'll have twice as much money as she has. How much money does she
have?

Answer 1

• $44 and $34

Explanation:

The amounts are x (me) and y (sister).

If I give my sister 5 dollars, then we will have the same amount of money:

• x - 5 = y + 5 ⇒ x = y + 10

If she gives me 8 dollars, then I'll have twice as much money as she has:

• x + 8 = 2(y - 8) ⇒ x + 8 = 2y - 16 ⇒ x = 2y - 24

Compare the equations and solve for y:

• y + 10 = 2y - 24
• 2y - y = 10 + 24
• y = 34

Find x:

• x = 34 + 10
• x = 44