the sum of two numbners is 143. on of the numbers is 3 more than six times the other number..find the two number and show work
To find the two numbers, let's assign variables to them. Let's say one number is x and the other number is y.
The problem states that the sum of the two numbers is 143, so we can write the equation: x + y = 143.
The problem also states that one of the numbers is 3 more than six times the other number. We can express this as an equation: x = 6y + 3.
Now we have a system of two equations:
1. x + y = 143
2. x = 6y + 3
To solve this system of equations, we can use the substitution method. We substitute equation 2 into equation 1:
(6y + 3) + y = 143
Simplifying the equation:
7y + 3 = 143
7y = 143 - 3
7y = 140
y = 140 / 7
y = 20
Now that we know y = 20, we can substitute this value back into equation 2 to find x:
x = 6(20) + 3
x = 120 + 3
x = 123
Therefore, the two numbers are x = 123 and y = 20.
one number --- x
the other number --- 6x + 3
x + 6x+3 = 143
7x = 140
x= 20
one is 20 the other is 123