Respuesta :
Answer:
In 28 days George have the same amount of candy as Penelope.
Step-by-step explanation:
Given:
Penelope has 152 pieces of candy.
George has 124 pieces of candy.
Penelope eats 5 pieces each day.
George eats 4 pieces each day.
To find in how many days will George have the same amount of candy as Penelope.
Solution:
Let the number of days in which George have the same amount of candy as Penelope be = [tex]x[/tex]
Using unitary method.
If Penelope eat 5 pieces of candy in 1 day.
In [tex]x[/tex] days, he will eat = [tex]5x[/tex] candies
Thus, after [tex]x[/tex] days number of candies left with Penelope = [tex]152-5x[/tex]
If George eat 4 pieces of candy in 1 day.
In [tex]x[/tex] days, he will eat = [tex]4x[/tex] candies
Thus, after [tex]x[/tex] days number of candies left with George = [tex]124-4x[/tex]
Since, in [tex]x[/tex] days George have the same amount of candy as Penelope, so we have:
[tex]124-4x=152-5x[/tex]
Solving for [tex]x[/tex]
Adding [tex]5x[/tex] both sides.
[tex]124-4x+5x=152-5x+5x[/tex]
[tex]124+x=152[/tex]
Subtracting 124 both sides.
[tex]124-124+x=152-124[/tex]
∴ [tex]x=28[/tex]
Thus, in 28 days George have the same amount of candy as Penelope.
