The sum of two numbers is 20. The larger number is four less than twice the smaller number. What are the two numbers?
4 Answers
hala718 | High School Teacher | (Level 1) Educator Emeritus
Assume that the numbers are x and y.
==> x+y=20....(1)
x=2y-4
Substitute with x=2y-4 in equation(1):
(2y-4)+y=20
3y-4 =20
ADD 4:
3y=24
Divide by 3:
y=24/3=8
==> x=2(8)-4 = 12
To check:\
12+8 = 20
12= 2(8)-4 =12
pohnpei397 | College Teacher | (Level 3) Distinguished Educator
Let x be the bigger number and let y be the smaller number.
x + y = 20
x = 2y -4
So now we substitute this value of x into the original equation.
2y - 4 + y = 20
3y - 4 = 20
3y = 24
y = 8
If y = 8, then
x = 12
because x + y must equal 20. To check this, let us see if these values work with the other equation
12 = (2*8) - 4
12 = 16 - 4
True -- so this is correct.
krishna-agrawala | College Teacher | (Level 3) Valedictorian
let x be the larger of the two numbers, and y be the other number.
Then:
x + y = 20 ... (1)
and
x = 2y - 4
Shifting the term 2y in above equation from right to left hand side we get:
x - 2y = -4 ... (2)
Subtracting equation (2) from equation (1) we get:
x - x + y + 2y = 20 + 4
3y = 24
Therefore:
y = 24/3 = 8
Substituting this value of y in equation (1) we get:
x + 8 = 20
x = 20 - 8 = 12
Answer:
Two numbers are 12 and 8.
neela | High School Teacher | (Level 3) Valedictorian
Let the smaller number be x.
Then the larger number is 4 times x = 4x.
The sum of the two numbers = x+4x= 5x but this is given to be 20. So 5x = 20. Therefore, x = 20/5 = 4 is the smaller number. The larger number 4x , therefore, is 4*4 = 20