The mystery of missing sweets
Sophie has a box of sweets. She gives half of them to her friend Emma. Then she eats 6 sweets herself. After that, she gives a third of what’s left to her brother. Finally, she is left with 10 sweets.
How many sweets did Sophie have at the start?
Let the total number of sweets Sophie had at the start be x.
ReplyDeleteStep 1:
She gives half to Emma:
Remaining = x ÷ 2
Step 2:
She eats 6 sweets:
Remaining = (x ÷ 2) - 6
Step 3:
She gives a third of what's left to her brother:
She gives away: (1/3) × ((x ÷ 2) - 6)
Remaining = (2/3) × ((x ÷ 2) - 6)
This is equal to 10 sweets:
(2/3) × ((x ÷ 2) - 6) = 10
Now solve the equation:
Step 4:
Multiply both sides by 3 to eliminate the denominator:
2 × ((x ÷ 2) - 6) = 30
Expand the brackets:
2 × (x ÷ 2) - 2 × 6 = 30
x - 12 = 30
Add 12 to both sides:
x = 42