Respuesta :
Answer:
10 candies on
Step-by-step explanation:
On Monday, Irina ate some candies. ( let it be [tex]x[/tex] )
On Tuesday, she ate twice as many as she did on Monday, ( [tex]2x[/tex] )
On Wednesday, she ate a third as many as she did on Tuesday means,
[tex]2x\times\frac{1}{3}[/tex] = [tex]\frac{2x}{3}[/tex]
On Thursday, she ate five more than she did on Wednesday means
[tex]\frac{2x}{3} +5[/tex]
On Friday, she ate two fewer candies than she did on Thursday means
[tex]\frac{2x}{3} +5 -2[/tex]
She ate the same number of candies on Friday as she did on Monday which is given means,
[tex]\frac{2x}{3} +5 -2 = x[/tex]
[tex]\frac{2x}{5} +3 = x[/tex]
By subtracting both side by [tex]\frac{2x}{5}[/tex]
[tex]\frac{2x}{5} - \frac{2x}{5} + 3 = x - \frac{2x}{5}[/tex]
[tex]3 = \frac{5x-2x}{5}\\ 3 = \frac{3x}{5}[/tex]
By cross multiplication:
[tex]3\times5 = 3x \\15 = 3x[/tex]
By dividing both sides by 3
[tex]\frac{15}{3} = \frac{3x}{3} \\5 = x[/tex]
On Tuesday, she ate twice as many as she did on Monday, ( [tex]2x[/tex] ) = [tex]2\times5 = 10[/tex]
Therefore, Irina ate 10 candies on Tuesday.
