Christine originally collected 60 toys
Step-by-step explanation:
Christine collected some toys for a charity.
We need to find how many toys Christine originally collected
Assume that Christine originally collected x toys
∵ Christine originally collected x toys
∵ She donated 3/4 of the toys to charity A
∵ [tex]\frac{3}{4}*x[/tex] = [tex]\frac{3}{4}x[/tex]
∴ She donated [tex]\frac{3}{4}x[/tex] to charity A
∴ The remaining = x - [tex]\frac{3}{4}x[/tex]
- Change x to [tex]\frac{4}{4}x[/tex] to make same denominators
∴ The remaining = [tex]\frac{4}{4}x[/tex] - [tex]\frac{3}{4}x[/tex]
∴ The remaining = [tex]\frac{1}{4}x[/tex]
∵ She donated 1/3 of the remaining toys to charity B
∵ The remainder = [tex]\frac{1}{4}x[/tex]
∵ [tex]\frac{1}{3}[/tex] × [tex]\frac{1}{4}x[/tex] = [tex]\frac{1}{12}x[/tex]
∴ She donated [tex]\frac{1}{12}x[/tex] to charity B
∴ The remaining = [tex]\frac{1}{4}x[/tex] - [tex]\frac{1}{12}x[/tex]
- Multiply the first fraction by 3 up and down to make same
denominators
∴ The remaining = [tex]\frac{3}{12}x[/tex] - [tex]\frac{1}{12}x[/tex]
∴ The remaining = [tex]\frac{2}{12}x[/tex]
- Simplify it by divide up and down by 2
∴ The remaining = [tex]\frac{1}{6}x[/tex]
∵ Christine had 10 toys left
- Equate the remaining by 10
∴ [tex]\frac{1}{6}x[/tex] = 10
- Multiply both sides by 6
∴ x = 60
Christine originally collected 60 toys
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