Final answer:
To find two consecutive integers such that five times the first integer is fifteen more than three times the second integer, we can set up and solve a system of equations. The first integer is 9 and the second integer is 10.
Step-by-step explanation:
To find two consecutive integers such that five times the first integer is fifteen more than three times the second integer, we can represent the problem as a system of equations. Let's call the first integer x and the second integer x+1.
We can set up the following equation: 5x = 3(x+1) + 15.
Simplifying the equation, we get 5x = 3x + 3 + 15, which becomes 5x = 3x + 18.
Subtracting 3x from both sides of the equation, we get 2x = 18.
Dividing both sides of the equation by 2, we find that x = 9.
So the first integer is 9, and the second integer is 9+1 = 10. Therefore, the two consecutive integers that satisfy the given condition are 9 and 10.