Question

Solve by algebra substitution 1. The sum of two number is 14 and their difference is 2. Find the numbers. 2. If twice the age of son is added to age of father, the sum is 56. But if twice the age of the father is added to the age of son, the sum is 82. Find the ages of father and son.

Answer 1

Explanation:

1) let the numbers be represented by x and y.

The sum of two number is 14. This means that

x + y = 14

The difference of the two numbers is 2. This means that

x - y = 2

x = y + 2

Substituting x = y + 2 into x + y = 14, it becomes

y + 2 + y = 14

2y + 2 = 14

2y = 14 - 2 = 12

y = 12/2 = 6

x = y + 2 = 6 + 2

x = 8

The numbers are 6 and 8

2) let x represent the age of the son.

Let y represent the age of the father.

If twice the age of son is added to age of father, the sum is 56. This means that

2x + y = 56

y = 56 - 2x

But if twice the age of the father is added to the age of son, the sum is 82. This means that

2y + x = 82 - - - - - - - - -1

Substituting y = 56 - 2x into equation 1, it becomes

2(56 - 2x) + x = 82

112 - 4x + x = 82

- 4x + x = 82 - 112

- 3x = - 30

x = - 30/ - 3

x = 10

y = 56 - 2x = 56 - 2 × 10

y = 56 - 20

y = 36

The father is 36 years and the son is 10 years old.