Two numbers differ by 9. 4 times the smaller is 5 more then twice the larger. Find the numbers.
if x is the smaller,
4x = 5+2(x+9)
x = 23/2
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 in the problem:
1. Two numbers differ by 9: This can be translated into the equation y - x = 9.
2. 4 times the smaller is 5 more than twice the larger: This can be translated into the equation 4x = 2y + 5.
Now, we have a system of two equations with two variables. To solve for x and y, we can use the method of substitution or elimination.
Let's solve it using the substitution method:
1. Rearrange equation 1 to get y = x + 9.
2. Substitute this value of y into equation 2: 4x = 2(x + 9) + 5.
3. Simplify equation 2: 4x = 2x + 18 + 5.
4. Combine like terms: 4x = 2x + 23.
5. Subtract 2x from both sides: 2x = 23.
6. Divide both sides by 2: x = 11.5.
Now that we have x, we can substitute it back into equation 1 to find y:
y = x + 9
y = 11.5 + 9
y = 20.5
So, the smaller number is 11.5 and the larger number is 20.5.