The sum of two numbers is 94.6. If one number is 19 times the other, what are the two numbers? Please explain how to solve. Thanks
The sum of two numbers is 94.6. If one number is 19 times the other, what are the two numbers?
smaller number:
bigger number:
n + 19n = 94.6
20n = 94.6
n = 4.73
let the bigger number be n
n+19n = 94.6
20n= 94.6
n= 94.6/20
n= 4.73
4.73+n= 94.6
n= 94.6- 4.73
n= 89.87
smaller number= 4.73
bigger number= 89.87
let the bigger number be n
n+19n = 94.6
20n= 94.6
n= 94.6/20
n= 4.73
4.73+n= 94.6
n= 94.6- 4.73
n= 89.87
smaller number= 4.73
bigger number= 89.87
sum = 94.6
Well, well, well, we've got ourselves a little math problem here. Let's see if I can clown around with the numbers and find the answer for you.
So, we need to find two numbers whose sum is 94.6. Let's call one number "x" and the other number "y." According to the problem, "x" is 19 times "y."
Now, the sum of "x" and "y" is 94.6, which we can write in an equation as:
x + y = 94.6
But we also know that "x" is 19 times "y." So, we can write this as:
x = 19y
Now we have a system of equations to solve. We can substitute the value of "x" from the second equation into the first equation:
19y + y = 94.6
Combine like terms:
20y = 94.6
And now, we can solve for "y":
y = 94.6 / 20
*yanky-doodle-doo*
y = 4.73 (approx.)
Okay, now that we've got the value of "y," let's substitute it back into the second equation to find the value of "x":
x = 19 * 4.73
*circus drumroll*
x = 89.87 (approx.)
So, the two numbers are approximately 89.87 and 4.73.
Now, that's no laughing matter. Maths can be quite a circus sometimes.
To solve this problem, let's assume that one number is x and the other number is y.
From the given information, we can form two equations based on the given conditions:
Equation 1: x + y = 94.6 (the sum of the two numbers is 94.6)
Equation 2: x = 19y (one number is 19 times the other)
Now, we can solve this system of equations using substitution or elimination method.
Substitution Method:
Start by substituting the value of x from Equation 2 into Equation 1:
19y + y = 94.6
20y = 94.6
Divide both sides by 20:
y = 94.6 / 20
y = 4.73
Now, substitute the value of y back into Equation 2:
x = 19 * 4.73
x = 89.87
Thus, the two numbers are approximately x = 89.87 and y = 4.73.
Explanation of the solution process:
1. First, we assign variables (x and y) to represent the two numbers we need to find.
2. Then, we create two equations based on the given information. In this case, we have one equation for the sum of the two numbers and another equation representing their relationship (one number being 19 times the other).
3. To solve the system of equations, we can use substitution or elimination method. Substitution involves solving one equation for one variable and substituting it into the other equation. Here, we substituted x = 19y into the equation for the sum of the two numbers.
4. After substituting, we have a single equation with one variable (y). Solving it will give us the value of y.
5. Once we have the value of y, we substitute it back into one of the original equations to find the corresponding value of x.
6. Finally, we find the values of both numbers (x and y) from the obtained solutions.