This is for the second question, which I will rewrite here:
Consecutive Integers. Find two consecutive integers such that the sum of twice the first integer and 3 times the second integer is 28. Write and solve that equation.
1. First, let's create variable to represent the 2 consecutive integers. Let's make "X" represent the smaller of the 2 numbers. Since the 2 integers are consecutive, which means they come right after another, we know that the second integer is "X+1".
For example, 3 and 4 are consecutive integers because they come one after another. If 3 was represented by X, then we know that the next consecutive integer is X + 1, or 3 +1, which equals 4!
2. Write out the equation. Just start building out the equation piece by piece as you read it:
"the sum of twice the first integer and..."
Remember, the first integer we represent as X. So twice the first integer is 2X.
"the sum of twice the first integer and 3 times the second integer"
So we know that we need to ADD the two components of the equation. And we know that the second integer is represented by "X+1", so we have:
2X + 3(X+1)
"...is 28."
So the equation equals 28:
2X + 3(X+1) = 28
3. Solve the equation:
2X + 3X + 3 = 28
5X + 3 = 28
5X = 25
X = 5
So we now know that first number, X, is equal to 5, and the next integer is X + 1, which is 6!
