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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?

Number: 

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