The disappearing number
When a number is doubled and then 7 is subtracted, the result is the same as when the number is tripled and then 17 is subtracted.
What is the number?
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Let the number of sweets Sophie started with be x.
ReplyDeleteGave half to Lucy:
Left with:
x ÷ 2
Gave a third of what's left to her brother:
A third of x ÷ 2 is x ÷ 6
After giving that away:
Remaining = x ÷ 2 - x ÷ 6
To subtract these, use a common denominator (6):
(3x - x) ÷ 6 = 2x ÷ 6 = x ÷ 3
Then she ate 6 sweets:
Remaining = x ÷ 3 - 6
This equals 10 sweets (what she has now):
x ÷ 3 - 6 = 10
Solve for x:
Add 6 to both sides:
x ÷ 3 = 16
Multiply both sides by 3:
x = 48