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"
Let's denote the larger number as L and the smaller number as S.
From the first statement, we can write the equation:
L = 2S - 7
From the second statement, we can write the equation:
L + S = 47
We can solve these two equations simultaneously to find the values of L and S.
Adding the two equations, we get:
L + L + S = 2S - 7 + 47
2L + S = 40
Now let's substitute L from the first equation into the second equation:
2(2S - 7) + S = 40
4S - 14 + S = 40
5S - 14 = 40
5S = 54
S = 10.8
Substituting this value back into the first equation:
L = 2(10.8) - 7
L = 21.6 - 7
L = 14.6
Therefore, the larger number (L) is approximately 14.6 and the smaller number (S) is approximately 10.8.
Let's represent the smaller number as x and the larger number as y.
From the first statement, we know that the larger number (y) is 7 less than twice the smaller number (2x). We can express this as an equation:
y = 2x - 7 (Equation 1)
From the second statement, we know that the sum of the two numbers (x + y) is 47. We can express this as another equation:
x + y = 47 (Equation 2)
Now we have a system of two equations:
Equation 1: y = 2x - 7
Equation 2: x + y = 47
To solve for x and y, we can use a method called substitution.
Step 1: Solve Equation 1 for y:
y = 2x - 7
Step 2: Substitute y in Equation 2 with 2x - 7:
x + (2x - 7) = 47
Step 3: Simplify and solve for x:
3x - 7 = 47
3x = 54
x = 18
Step 4: Substitute the value of x into Equation 1 to solve for y:
y = 2(18) - 7
y = 36 - 7
y = 29
Therefore, the smaller number is 18 and the larger number is 29.
The solution is:
x = 18
y = 29
To solve the given situation, let's assign variables to the two numbers. Let's call the larger number "L" and the smaller number "S".
1. "The larger of two numbers is 7 less than twice the smaller number":
This can be written as an equation:
L = 2S - 7
2. "The sum of two numbers is 47":
This can also be written as an equation:
L + S = 47
To find the values of L and S, we need to solve the system of equations formed by these two equations.
We can use substitution or elimination method to solve the system of equations. Let's use the substitution method:
From the equation L = 2S - 7, we can express L in terms of S:
L = 2S - 7
Substitute this value of L in the second equation:
(2S - 7) + S = 47
Now we can solve for S:
3S - 7 = 47
Add 7 to both sides:
3S = 54
Divide both sides by 3:
S = 18
Now that we have the value of S, substitute it back into the first equation to find L:
L = 2(18) - 7
L = 36 - 7
L = 29
So the two numbers are 18 and 29.