Word Problem

Question

The sum of three whole numbers is 7. The second number is 1 more than twice of the third number. The sum of the first and third number is 3 less than the second number. Find all the three numbers.

Answer 1

Let x, y, and z be the three whole numbers:

1. The sum of three whole numbers is 7: x+y+z=7
2. The second number (y) is 1 more than twice of the third number (z): y = 2z+1
3. The sum of the first (x) and third number (z) is 3 less than the second number (y): x+z = y-3

 

Solve for y:

x + y + z = 7            {equation 1}

x + z + y = 7            {rearrange (commutative law of addition)}

(y-3) + y = 7            {equation 3: x+z = y-3}

2y - 3 = 7

2y = 10

y = 5

 

Solve for z:

y = 2z+1                  {equation 2}

5 = 2z+1                  {y=5}

4 = 2z

2 = z

 

Solve for x:

x + y + z = 7

x + 5 + 2 = 7           {y=5, z=2}

x + 7 = 7

x=0

 

Check:

x+y+z=7             {Verify equation 1 is true}

0+5+2 = 7

7=7     Check!

 

y=2z+1               {Verify equation 2 is true}

5=2*2+1

5=4+1

5=5     Check!

 

x+z=y-3               {Verify equation 3 is true}

0+2=5-3

2=2      Check!

Answer 2

a,b,c are the numbers

 

The sum of three whole numbers is 7

a+b+c=7

 

The second number is 1 more than twice of the third number

b=2c+1

 

The sum of the first and third number is 3 less than the second number

a+c=b-3

 

see if this helps

Answer 3

Jim,

 

Great question, a classic SAT type.

 

The way to do these problems (and, really, any algebra problem) is to consider the unknown quantities as variables.

 

Here's what I mean. What if you called each number a, b, and c? What do you know about them?

 

Well, for certain you know that a + b + c = 7 ("the sum of three whole numbers is 7").

 

You know some other things too. Such as

 

b = 1 + 2 * c ("the second number is 1 more than twice of the third number")

 

What is the third thing you know?

 

When you get that, you'll have three equations. Three equations and three variables means you can solve for each!

 

Best of luck.

Answer 4

Lets set up some expressions and then some equations based on the given information.

1st number = x

2nd number = 2y+1

3rd number = y

 

Then we have       x + (2y+1) + y = 7

and                      x + y = (2y+1) - 3

 

Try getting all your x's and y's on one side of the equals sign, the numbers on the other side, and then employing the elimination method for solving systems of equations in 2 variables.  Be sure to find all three numbers, not just x and/or y.