I would let #1 = x.
Then #2 = x+1
#3 = x+2
#4 = x+3
The problem says we want the sum of the first three. That will be
x + (x + 1) + (x + 2) and that should be 60 more than the fourth. The fourth is x + 3; therefore, set them equal and add 60 to the fourth. Solve for x.
Post your work if you get stuck.
x+(x+1)+(x+2) = (x+3)+60
Find four consecutive integers such that the sum of the first three is 60 more than the fourth.
What is the best way to solve this?
The best way to solve this problem is by setting up and solving the equation given in the problem.
Let's follow the steps given in the problem:
Step 1: Let #1 = x.
Step 2: Then #2 = x + 1.
Step 3: #3 = x + 2.
Step 4: #4 = x + 3.
According to the problem, the sum of the first three numbers (#1, #2, and #3) is 60 more than the fourth number (#4).
So, let's set up the equation:
x + (x + 1) + (x + 2) = (x + 3) + 60
Now, we can solve this equation to find the value of x.
To solve this problem, you can follow the steps provided in the given explanation:
1. Assign a variable to represent the first number. In this case, let's call it "x".
2. Express the second, third, and fourth numbers in terms of x. According to the information, the second number is x + 1, the third number is x + 2, and the fourth number is x + 3.
3. Set up the equation using the given condition: "the sum of the first three is 60 more than the fourth."
The equation will be: x + (x + 1) + (x + 2) = (x + 3) + 60.
4. Simplify the equation by combining like terms on both sides.
x + x + 1 + x + 2 = x + 3 + 60.
3x + 3 = x + 63.
5. Move all terms involving x to one side of the equation by subtracting x from both sides.
3x - x + 3 = x - x + 63.
2x + 3 = 63.
6. Subtract 3 from both sides of the equation to isolate the term with x.
2x + 3 - 3 = 63 - 3.
2x = 60.
7. Divide both sides of the equation by 2 to solve for x.
2x / 2 = 60 / 2.
x = 30.
So, the value of x is 30. To find the four consecutive integers, substitute this value back into the expressions for each number:
The first number = 30,
The second number = 30 + 1 = 31,
The third number = 30 + 2 = 32,
The fourth number = 30 + 3 = 33.
Therefore, the four consecutive integers that satisfy the given conditions are 30, 31, 32, and 33.