The difference of two integers is 9. Five times the smaller is 7 more than three times the larger. Find the numbers.
5•s = 7+3b
To solve this problem, let's represent the two integers as variables. Let's call the smaller integer "x" and the larger integer "y".
According to the problem, the difference of the two integers is 9:
y - x = 9 ...equation (1)
It also states that five times the smaller integer is 7 more than three times the larger integer:
5x = 3y + 7 ...equation (2)
Now we have a system of two equations (equations 1 and 2) with two variables (x and y). We can solve this system of equations using a method called substitution or elimination.
Let's solve it using the substitution method:
1. Rearrange equation (1) to express "y" in terms of "x":
y = x + 9
2. Substitute this value of "y" in equation (2):
5x = 3(x + 9) + 7
3. Simplify and solve for "x":
5x = 3x + 27 + 7
5x = 3x + 34
2x = 34
x = 17
4. Substitute the value of "x" back into equation (1) to solve for "y":
y - 17 = 9
y = 26
Therefore, the two numbers are 17 and 26.