The larger of two consecutive integers is 7 greater than twice the smaller. Find the integers.
A) 4,5
B) -8,-9
C) -5,-6
integer 1 = a
integer 2 = b
b-a = 1 (b is one more than a)
b-7 = 2*a (b is seven more than two times a)
a = b-1
b-7 = 2*(b-1)
b-7 = 2b-2
b = -5
so a should be -6
answer is C)
To solve this problem, let's first define our variables. Let's call the smaller integer x, and the larger integer (which is 7 greater than twice the smaller) y.
From the given information, we have two conditions:
1. The larger integer is 7 greater than twice the smaller: y = 2x + 7.
2. The two integers are consecutive, which means that the larger integer is one more than the smaller: y = x + 1.
Now, we can set up a system of equations using these conditions:
Equation 1: y = 2x + 7
Equation 2: y = x + 1
Since both equations are equal to y, we can set them equal to each other:
2x + 7 = x + 1
Next, let's solve for x by subtracting x from both sides of the equation:
2x - x + 7 = x - x + 1
x + 7 = 1
To isolate x, we'll subtract 7 from both sides of the equation:
x + 7 - 7 = 1 - 7
x = -6
Now that we have x, we can substitute this value back into one of the original equations to find y.
Using Equation 2: y = x + 1
y = -6 + 1
y = -5
So, the two consecutive integers are -6 and -5.
Therefore, the correct answer is C) -5, -6.
Let's represent the smaller integer as "x" and the larger integer as "x+1".
According to the given information, we can set up the equation:
x+1 = 2x + 7
Now, let's solve for x:
x+1 = 2x + 7
Subtracting x from both sides:
1 = x + 7
Subtracting 7 from both sides:
-6 = x
So, the smaller integer is -6 and the larger integer is -6 + 1 = -5.
Therefore, the answer is option C) -5,-6.