The sum of 2 numbers is 208. One-third of the greater number equals the smaller number. What are the numbers?

Answer 1

Let x be the greater
Let y be the lesser number
x + y = 208
x/3 = y, or x/3 - y = 0
Add them:
x + x/3 = 208
x(4/3) = 208
x = 208(3/4) = 52*3 = 156
x/3 = 156/3 = 52

Answer 2

Let the Greater number be 'x'
So Smaller number equals to '1/3x'
Sum of two numbers is 208
x + x/3 = 208
(3x + x) = 208 * 3 (Multiplying by 3 on both sides)
4x = 624
x = 156.
So greater number is 156.
Smaller number is 156/3
i.e 52.

Answer 3

let the smaller no. be x
then the greater no. is 3x(according to given information)
also their sum is 208
therefore
x + 3x = 208
4x=208

x=52
therefore
smaller no. is x = 52
while bigger no. is 3x = 52 * 3 = 156

Answer 4

let x be the bigger number

x + (1/3)x = 208
(4/3)x = 208
x = 156

smaller number = 156/3 = 52

Answer 5

Assume that the two numbers are X and Y

X + Y = 208---------------------------- (1)
(1/3) X = Y---------------------------- (2)

Substitute (2) into (1)

X + (1/3) X = 208---------------------------- (3)

Multiply (3) with 3

3*{X + (1/3) X} = 3*208
3 X + X = 624
4 X = 624
X = 624 / 4
X = 156

Substitute the value of X into (2) to get the value of Y:-

(1/3)*156 = Y
Y = 52

Therefore, the numbers are: 156 and 52

Answer 6

*Algebraic Equations...
1. x + y = 208
2. (1/3)(x) = y

*Solve for "x" or "y" in either equation. Let's solve for "x" in the 1st equation.

First: subtract "y" from both sides...

x + y - y = 208 - y
x = 208 - y

*Replace "208 - y" with the x-variable in the 2nd equation...

(1/3)(208 - y) = y

*Distribute the outer term with the terms in parenthesis...

(1/3)(208) + (1/3)(- y) = y
(1*208)/3 - (1/3)y = y
208/3 - (1/3)y = y

Sec: eliminate fractions - multiply the denominator with both sides...

(3)(208/3) - (3)[(1/3)y] = (3)(y)

*Cross cancel "like" terms & combine the remaining terms...

208 - 1y = 3y
208 - y = 3y

*Combine "like" terms - add "y" with both sides...

208 - y + y = 3y + y
208 = 4y

Or, 4y = 208

Third: isolate "x" on one side - divide both terms by "4"...

4y/4 = 208/4
y = 208/4
y = 52

Fourth: replace "52" with the y-variable in the 1st equation...

x + 52 = 208

*Isolate "x" on one side - subtract 52 from both sides...

x + 52 - 52 = 208 - 52
x = 156

Solution: (156, 52)

Answer 7

x+y=208
x/3=y or
x=3y
x+y=208 substitute 3y for x
3y+y=208 combine like terms
4y=208 divide both sides by 4
y=52
x=3y=3*52=156

the numbers are 156 & 52

check
156+52=208

Answer 8

let the greater no. be x
let the smaller no. be y
x+y=208
1/3 of x=y
x+1/3x=208
4x/3=208
x=208*3/4
x=52*3
x=156

y=1/3x
y=1/3*156
y=52

the two numbers are 156 and 52

Answer 9

156 and 52

Answer 10

52 & 156