Solve the answers for the following situation (seperate answers with a and no spaces)
"The larger of two numbers is 7 less than twice the smaller number"
"the sum of two numbers is 47"
smaller number ,larger number
Let's assume that the smaller number is x and the larger number is y.
From the first statement, we can write the equation:
y = 2x - 7
From the second statement, we can write the equation:
x + y = 47
Now we have a system of two equations:
y = 2x - 7
x + y = 47
To solve this system, we can use the substitution method.
Substitute the value of y from the first equation into the second equation:
x + (2x - 7) = 47
3x - 7 = 47
3x = 54
x = 18
Now substitute the value of x back into the first equation to find y:
y = 2(18) - 7
y = 36 - 7
y = 29
Therefore, the smaller number is 18 and the larger number is 29.
Answer: 18 and 29
Let's solve the problem step-by-step.
1. "The larger of two numbers is 7 less than twice the smaller number."
Let's assume the smaller number as "x".
The larger number can be represented as "2x - 7".
2. "The sum of two numbers is 47."
The equation for this statement would be:
x + (2x - 7) = 47
Simplifying the equation:
x + 2x - 7 = 47
3x - 7 = 47
3x = 47 + 7
3x = 54
Dividing both sides of the equation by 3:
x = 18
Now we have found the value of the smaller number, which is 18.
3. Calculating the larger number:
Using the value of the smaller number, we substitute it in the equation:
2x - 7 = 2(18) - 7 = 36 - 7 = 29
The larger number is 29.
So the answers to the problem are:
Smaller number: 18
Larger number: 29
To solve this situation, we will use a system of equations. Let's denote the smaller number as x and the larger number as y.
1. "The larger of two numbers is 7 less than twice the smaller number":
This can be translated into the equation:
y = 2x - 7
2. "The sum of two numbers is 47":
This can be translated into the equation:
x + y = 47
To find the solution, we can substitute equation (1) into equation (2):
x + (2x - 7) = 47
Simplifying the equation:
3x - 7 = 47
Add 7 to both sides:
3x = 54
Divide both sides by 3:
x = 18
Now that we have the value of x, we can substitute it back into equation (2) to find y:
18 + y = 47
Subtract 18 from both sides:
y = 29
Therefore, the smaller number is 18 and the larger number is 29.