Suppose 3b-4a=24. Given that a and b are consecutive integers, and b<a, what is the value of b?
Well, since a and b are consecutive integers, that means their difference is 1. So we can write the equation as 3(b-1) - 4b = 24. Simplifying this equation, we get 3b - 3 - 4b = 24. Combining like terms, we get -b - 3 = 24. Adding 3 to both sides, we have -b = 27. Multiplying both sides by -1, we get b = -27.
So, the value of b is -27. But hey, chin up! Negative numbers need love too!
To find the value of b, we can use the information given in the equation and the relationship between a and b.
Let's start by understanding what is meant by "consecutive integers." Consecutive integers are numbers that follow each other in order, with a difference of 1 between them. For example, 1, 2, 3, 4, and so on.
In this problem, we are given that a and b are consecutive integers, and b < a. This means that the value of b is one less than a.
We are also given the equation 3b - 4a = 24.
Now, let's substitute b with a - 1 in the equation since b is one less than a:
3(a - 1) - 4a = 24.
Distribute the 3 to both terms inside the parentheses:
3a - 3 - 4a = 24.
Combine like terms:
-a - 3 = 24.
Now, add 3 to both sides of the equation to isolate the negative term:
-a - 3 + 3 = 24 + 3.
Simplify:
-a = 27.
To solve for a, multiply both sides of the equation by -1 to eliminate the negative sign:
-a * (-1) = 27 * (-1).
Simplify:
a = -27.
But wait, we know that b < a. Since a = -27, b must be lesser than -27. Since we are dealing with consecutive integers, the only possibility is that b = -28.
Therefore, the value of b is -28.
Nope her answer is correct not yours.
She wrote the same thing so yeah.
the keyword is consecutive, meaning the numbers are one apart
since a > b
a = b+1
3b-4a=24
3b - 4(b+1) = 24
-b = 28
b = -28
check:
then a = -28+1 = -27
3b-4a
= 3(-28) - 4(-27)
= 24 , my answer is correct