two numbers are such that twice the larger number differstfrom thrice the smaller number by four the sum of two number is 17 find the number
larger --- x
smaller ---- y
the sum of two number is 17 ----> x+y=17
twice the larger number ---> 2x
thrice the smaller number ---> 3y
twice the larger number differs from thrice the smaller number by four
-----> 2x - 3y = 4
from x + y = 17 , we get y = 17-x
sub into the 2nd
2x - 3y = 4
2x - 3(17-x) = 4
2x - 51 + 3x = 4
5x = 55
x = 11 , then y = 17-11 = 6
To solve this problem, we can use a system of equations. Let's assign variables to the two numbers and set up the equations based on the given information.
Let:
- The larger number be represented by "L"
- The smaller number be represented by "S"
From the given information, we can create the following equations:
1) Twice the larger number differs from thrice the smaller number by four:
2L = 3S + 4
2) The sum of the two numbers is 17:
L + S = 17
Now we have a system of equations. We can solve it using different methods. Let's use the substitution method to solve this system.
Step 1: Solve one equation for one variable (in terms of the other variable).
From equation 2, we can solve for L:
L = 17 - S
Step 2: Substitute the value of L in terms of S into equation 1.
2(17 - S) = 3S + 4
Step 3: Simplify and solve for S:
34 - 2S = 3S + 4
Collect like terms:
-2S - 3S = 4 - 34
-5S = -30
Divide both sides by -5:
S = -30 / -5
Simplifying gives:
S = 6
Step 4: Substitute the value of S into equation 2 to solve for L:
L + 6 = 17
L = 17 - 6
L = 11
So, the larger number (L) is 11, and the smaller number (S) is 6.
X=2
Let's assume the larger number is 'x' and the smaller number is 'y'.
According to the given information:
1) Twice the larger number differs from thrice the smaller number by four:
2x = 3y + 4
2) The sum of the two numbers is 17:
x + y = 17
We can solve this system of equations to find the values of x and y.
Let's solve equation (2) for x:
x = 17 - y
Now we substitute the value of x in equation (1):
2(17 - y) = 3y + 4
34 - 2y = 3y + 4
Next, we simplify the equation:
34 - 4 = 3y + 2y
30 = 5y
Dividing both sides of the equation by 5:
y = 6
Now substitute the value of y in equation (2) to find x:
x + 6 = 17
x = 17 - 6
x = 11
So, the larger number is 11 and the smaller number is 6.