the smaller of two numbers is 18 less than the larger number. If 5 timnes the larger number esxceeds four times the smaller by 100. Find the numbers.
s = L -18
5L - 4s = 100
Substitute L-18 for s in the second equation and solve for L. Insert that value into the first equation to solve for s. Check by putting both values into the second equation.
s = 114
L = 172
To solve this problem, let's assign variables to the unknown numbers. Let's call the smaller number "x" and the larger number "y".
We are given two pieces of information:
1. "The smaller of two numbers is 18 less than the larger number."
This can be expressed as: x = y - 18.
2. "If 5 times the larger number exceeds four times the smaller by 100."
This can be expressed as: 5y = 4x + 100.
Now we have a system of two equations:
Equation 1: x = y - 18
Equation 2: 5y = 4x + 100
We can solve this system using substitution or elimination.
Let's solve it using substitution:
Substitute the value of x from Equation 1 into Equation 2:
5y = 4(y - 18) + 100
Simplify the equation:
5y = 4y - 72 + 100
5y = 4y + 28
Subtract 4y from both sides:
y = 28
Now substitute the value of y back into Equation 1 to find x:
x = 28 - 18
x = 10
Therefore, the smaller number is 10 and the larger number is 28.