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"
the smaller number+larger number=sum
Let's represent the smaller number as "x" and the larger number as "y".
According to the first statement, the larger number is 7 less than twice the smaller number:
y = 2x - 7
According to the second statement, the sum of the two numbers is 47:
x + y = 47
Now, we can solve this system of equations by substituting the value of y from the first equation into the second equation:
x + (2x - 7) = 47
Combining like terms:
3x - 7 = 47
Adding 7 to both sides:
3x = 54
Dividing both sides by 3:
x = 18
Now, substitute this value of x back into the first equation to find y:
y = 2(18) - 7
y = 36 - 7
y = 29
So, the smaller number is 18 and the larger number is 29.
Let's solve the situation step-by-step:
1. "The larger of two numbers is 7 less than twice the smaller number."
Let's represent the smaller number as x. According to the given information, the larger number can be represented as 2x - 7.
2. "The sum of two numbers is 47."
The sum of the two numbers is given as 47, which means x + (2x - 7) = 47.
3. Now, we'll solve the equation to find the values of x and the larger number:
Substituting (2x - 7) for the larger number, we get x + (2x - 7) = 47.
Combining like terms, 3x - 7 = 47.
Adding 7 to both sides, 3x = 54.
Dividing both sides by 3, x = 18.
4. Calculate the larger number:
The larger number is 2x - 7, so substituting x with 18, we get 2(18) - 7 = 36 - 7 = 29.
5. Calculate the sum of the smaller and larger numbers:
The sum of the smaller and larger numbers is x + (2x - 7), which is 18 + 29 = 47.
Therefore, the smaller number is 18, and the larger number is 29.
To solve the given situation, let's represent 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":
We can write this statement as: y = 2x - 7.
2) "The sum of two numbers is 47":
This can be represented as: x + y = 47.
Now, we have a system of equations:
Equation 1: y = 2x - 7
Equation 2: x + y = 47
To find the values of x and y, we can use the method of substitution or elimination.
Let's use the method of substitution:
From Equation 1, isolate y:
y = 2x - 7
Substitute this value of y into Equation 2:
x + (2x - 7) = 47
Simplify the equation:
3x - 7 = 47
Add 7 to both sides of the equation:
3x = 54
Divide both sides by 3:
x = 18
Now substitute this value of x into Equation 1 to find y:
y = 2(18) - 7
y = 36 - 7
y = 29
Therefore, the smaller number (x) is 18, and the larger number (y) is 29.
Final Answer: 18a29