# The sum of two numbers is 66

The sum of two numbers is 66. Two times the larger number minus the smaller number is 177. What are the numbers?

The sum of two numbers is 66. We can represent the numbers as follows:

x = the bigger number

y = the smaller number

Thus,

x + y = 66 (Eq1)

Two times the larger number minus the smaller number is 117. Thus, we derives equations:

2x - y = 117 (Eq2)

Solving for y in Eq2 gives:

2x - y = 117

2x - 117 = y (Eq3)

Substituting Eq3 in Eq1 gives:

x + y = 66

x + (2x - 117) = 66

x + 2x - 117 = 66

3x - 117 = 66

3x = 66 + 117

3x = 183

x = 183/3

x = 61

Therefore, the bigger number is 61.

To solve for y, substitute 61 in Eq1, giving:

x + y = 66

61 + y = 66

y = 66 - 61

y = 5

Therefore, the smaller number is 5.

CHECK:

Eq1: x + y = 66

61 + 5 = 66

66 = 66

Eq2: 2x - y = 117

2(61) - 5 = 117

117 = 117

## The sum of two numbers

The sum of two numbers is 66. We can represent the numbers as follows:

x = the bigger number

y = the smaller number

Thus,

x + y = 66 (Eq1)

Two times the larger number minus the smaller number is 117. Thus, we derives equations:

2x - y = 117 (Eq2)

Solving for y in Eq2 gives:

2x - y = 117

2x - 117 = y (Eq3)

Substituting Eq3 in Eq1 gives:

x + y = 66

x + (2x - 117) = 66

x + 2x - 117 = 66

3x - 117 = 66

3x = 66 + 117

3x = 183

x = 183/3

x = 61

Therefore, the bigger number is 61.

To solve for y, substitute 61 in Eq1, giving:

x + y = 66

61 + y = 66

y = 66 - 61

y = 5

Therefore, the smaller number is 5.

CHECK:

Eq1: x + y = 66

61 + 5 = 66

66 = 66

Eq2: 2x - y = 117

2(61) - 5 = 117

117 = 117

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