The ratio of Ali's stickers to Bala's stickers is 3 : 7. After Bala gave 42 stickers to Ali, they had an equal number of stickers. How many stickers did Ali have at first?
Question
The ratio of Ali's stickers to Bala's stickers is 3 : 7. After Bala gave 42 stickers to Ali, they had an equal number of stickers. How many stickers did Ali have at first?
Solution
Let's solve this step by step:
Step 1: Let's assume the number of stickers Ali and Bala originally had were 3x and 7x respectively.
Step 2: According to the problem, Bala gave 42 stickers to Ali, which made their number of stickers equal. This means that Bala's stickers decreased by 42 and Ali's stickers increased by 42.
Step 3: So, we can set up the equation 3x + 42 = 7x - 42.
Step 4: Solving this equation, we get 4x = 84.
Step 5: Solving for x, we get x = 21.
Step 6: To find the number of stickers Ali had at first, we multiply x by 3 (since Ali had 3x stickers). So, Ali had 3 * 21 = 63 stickers at first.
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