Two whole numbers $A$ and $B$ satisfy the following conditions. Find $A$ and $B$ .
$A-B=25$
$A:B$ is equivalent to $13:8$ .
It is annoying and my teacher doesn't teach me how to do it. Please help me with this one.
What is also annoying is all that strange typing.
I think what you are trying to say is:
A - B = 25
A : B = 3 : 8
let A = 3x and B = 8x
then A - B = 25
3x - 8x = 25
-5x = 25
x = -5
so A = 3x = -15 , and B = 8x = -40
Question
Two whole numbers A and B satisfy the following conditions. Find A and B.
A+B=44
A:B is equivalent to 4:7.
To find the values of $A$ and $B$, we can set up a system of linear equations using the given information.
Let's start by using the first condition, $A-B=25$. Since the difference between $A$ and $B$ is 25, we can write this equation as:
$A = B + 25 \quad \text{(Equation 1)}$
Now let's use the second condition, which states that the ratio of $A$ to $B$ is equivalent to $13:8$. We can express this as:
$\frac{A}{B} = \frac{13}{8} \quad \text{(Equation 2)}$
To solve the system of equations, we can substitute Equation 1 into Equation 2. Substituting $A = B + 25$ in Equation 2, we get:
$\frac{B + 25}{B} = \frac{13}{8}$
To simplify our equation, we can cross-multiply:
$8(B + 25) = 13B$
Expanding and simplifying the equation, we have:
$8B + 200 = 13B$
Rearranging the terms, we get:
$5B = 200$
Dividing both sides by 5, we find:
$B = 40$
Now, substitute the value of $B$ back into Equation 1 to find $A$:
$A = B + 25 = 40 + 25 = 65$
Therefore, the values of $A$ and $B$ that satisfy the given conditions are $A = 65$ and $B = 40$.