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 = ![x](https://tex.z-dn.net/?f=x)
Using unitary method.
If Penelope eat 5 pieces of candy in 1 day.
In
days, he will eat =
candies
Thus, after
days number of candies left with Penelope = ![152-5x](https://tex.z-dn.net/?f=152-5x)
If George eat 4 pieces of candy in 1 day.
In
days, he will eat =
candies
Thus, after
days number of candies left with George = ![124-4x](https://tex.z-dn.net/?f=124-4x)
Since, in
days George have the same amount of candy as Penelope, so we have:
![124-4x=152-5x](https://tex.z-dn.net/?f=124-4x%3D152-5x)
Solving for ![x](https://tex.z-dn.net/?f=x)
Adding
both sides.
![124-4x+5x=152-5x+5x](https://tex.z-dn.net/?f=124-4x%2B5x%3D152-5x%2B5x)
![124+x=152](https://tex.z-dn.net/?f=124%2Bx%3D152)
Subtracting 124 both sides.
![124-124+x=152-124](https://tex.z-dn.net/?f=124-124%2Bx%3D152-124)
∴ ![x=28](https://tex.z-dn.net/?f=x%3D28)
Thus, in 28 days George have the same amount of candy as Penelope.