The sum of two numbers is 104. Their difference is 6. Find the numbers.

y = 49

x = 55

the numbers are 49 and 55

Step-by-step explanation:

let the numbers be x and y

the sum of the two number is 104 implies

x + y = 104

the difference of the two number is 6 implies

x - y = 6

so we will say that let

x + y = 104 ... equation 1

x - y = 6 ... equation 2

from equation 2

x - y = 6 ... equation 2

x = 6 + y ... equation 3

put the value of x = 6 + y in equation 1

x + y = 104 ... equation 1

6+y + y = 104

6 + 2y = 104

2y = 104-6

2y = 98

divide both sides by the coefficient of y which is 2

2y/2 = 98/2

y = 49

substitute for y = 49 in equation 3

x = 6 + y ... equation 3

x = 6 + 49

x = 55

therefore the two numbers are 55 and 49 respectively

49 and 55

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