Question

A and B both have some pencils. if A gives 10 pencils to B, then B will have twice as many as A. And if B gives 10 pencils to A, then they will have the same number of pencils. How many pencils does each have?

Answer 1

Let A has x pencils

Let B has y pencils

If A gives 10 pencils to B , then B will have twice as many as A

2(x - 10) = y + 10

2x - 20 = y + 10

y = 2x - 30 --------------------------- [ 1 ]

If B gives 10 pencils to A , then they will have the same number of pencils

x + 10 = y - 10

y = x + 20 --------------------------- [ 2 ]

Equate equation [ 1 ] and equation [ 2 ]:

2x - 30 = x + 20

x = 50 --------------------------- sub into [ 1 ] to find y

y = 2x - 30

y = 2(50) - 30

y = 70

Find the number of pencils each have:

A = x = 50

B = y = 70

Answer: A has 50 pencils and B has 70 pencils