The larger of two numbers is 1 less than 3 times the smaller number. If twice the smaller number is increased by the larger number, the result is 18 more than the larger number.Find both numbers
Let's denote the larger number as L and the smaller number as S.
We are given two pieces of information:
1. The larger number is 1 less than 3 times the smaller number, which can be expressed as L = 3S - 1.
2. Twice the smaller number increased by the larger number results in 18 more than the larger number, which can be written as 2S + L = L + 18.
To find both numbers, we can set up a system of equations using these two equations:
Equation 1: L = 3S - 1
Equation 2: 2S + L = L + 18
Now, let's solve the system of equations:
Substitute Equation 1 into Equation 2:
2S + (3S - 1) = (3S - 1) + 18
Simplify Equation 2:
2S + 3S - 1 = 3S + 17
Combine like terms:
5S - 1 = 3S + 17
Move all terms with S to one side and constants to the other side:
5S - 3S = 17 + 1
2S = 18
Divide both sides by 2 to solve for S:
S = 9
Now substitute the value of S back into Equation 1 to find L:
L = 3S - 1
L = 3(9) - 1
L = 27 - 1
L = 26
Therefore, the smaller number is 9 and the larger number is 26.
If the two numbers are x and y, then
y = 3x-1
2x+y = y+18
Now just solve for x and y