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

Question

An algebraic word problem.
I need a little help.
I'm not that great at it.
Help me!!!

Answer 1

[06]
Let the numbers be x and 208-x
According to the problem
x/3=208-x
x=624-3x[multiplying both sides by 3]
x+3x=624
4x=624
x=624/4=156
Therefore the numbers are 156 and 208-156=52

Answer 2

its telling you that the greater number needs to be divided into 3 parts to find the solution of the smaller number
you dont know that number but you know the sum which is 208, which would be divided into 4 parts (the 4th part being the lesser number). If we call each of these unknown parts x
then the lesser number would be x and the greater number would be 3x

3x+x =208
4x =208
4x/4 = 208/4 (what you do to one side to isolate the x you do to the other side of the = sign)

x = 52 the lesser number
3x = 156 the greater number
52 + 156 = 208

Answer 3

Call the smaller number "p." Since we know that the 1/3 of the larger number equals the smaller number, p, then multiplying p by 3 must result in the larger number, so the larger number can be expressed as "3p."

Their sum is 208, so we say

p + 3p = 208
4p = 208
p = 208/4
p = 52

Now we know that the smaller number is 52, and finding the larger number is easy--just multiply the smaller number by 3, to get 156. You can check by adding 52 and 156, and they equal 208.

Answer 4

You can do this one without explicit algebra, if you think about it.

Given the instructions, the larger number must be three times the smaller. Hence the entire number, 208, is four times the smaller number. This means the smaller number is 208 divided by four, or 52; and from that you can get the other number by subtraction (208 - 52) or by multiplication (52 * 3).

Answer 5

This is a systems of equations problem.

First equation: x + y = 208
2nd Equation: x = 3y

Now you have both equations, so you need to substitute for one to get a single variable. Since you know that x = 3y, subsitute 3y for x in the 1st equation:

3y + y = 208
4y = 208
y = 52
x = 52 * 3= 156

y = 52
x = 156

Answer 6

x = greater
y = smaller

1/3x = y
x + y = 208
substitute
x + 1/3x = 208
4/3 x = 208
x = 156 substitute again
156 + y = 208
y = 52
x = 156

Answer 7

156, 52

Answer 8

x + y = 208

1/3x = y

x + 1/3x = 208

3 * (x + 1/3x) = 3 * 208

3x + x = 624

4x = 624

4x/4 = 624/4

x = 156
y = 52

Answer 9

So state it in algebraic form first.
x + y = 208
1/3y (or x) = x (or y)
x + 3x = 208
4x = 208
x = 52
y = 156

Answer 10

52 and 156