Question

the sum of 3 numbers is 245. the 2nd number is 7 less than the first, and the third is 4 more than first. What are the Numbers?

Answer 1

the first number is 248/3, second number is 227/3, third number is 260/3

Explanation:

You can answer this question with the aid of equations.

We know that the three numbers add up to 245.

a = first number

b = second number

c = third number

a + b + c = 245

a = b + 7

c = a + 4

substitute in the second equation into the third.

c = b + 7 + 4

simplify

c = b + 11

substute the second and the new equation into the first equation

b + 7 + b + b + 11 = 245

simplify

3b + 18 = 245

3b = 227

b = 227/3

substitue b into the second equation

a = 248/3

c = 260/3

so the first number is 248/3, second number is 227/3, third number is 260/3

Answer 2

First, second and third numbers are:

`\sf (248)/(3) ,(221)/(3) \textsf{ and } (260)/(3)` respectively.

Explanation:

In order o solve this problem, we can use the following system of equations:

Let the three number be x, y and z respectively.

According to the question, we have:

• x + y + z = 245
• y = x - 7
• z = x + 4

We can substitute the second and third equations into the first equation to get a single equation in terms of x:

x + (x - 7) + (x + 4) = 245

Simplify like terms:

3x - 3 = 245

Add 3 on both sides:

3x - 3 + 3 = 245 + 3

3x = 248

Divide both sides by 3.

`\sf (3x)/(3)=(248)/(3)`

`\sf x =(248)/(3)`

Now that we know the value of x, we can substitute it back into the second and third equations to find the values of y and z:

`\sf y = x -7 = (248)/(3) -7= ( 248-7* 3 )/(3) =(221)/(3)`

`\sf z = x + 4 = = (248)/(3) +4 = ( 248+4* 3 )/(3) =(260)/(3)`

Therefore, the three first, second and third numbers are:

`\sf (248)/(3) ,(221)/(3) \textsf{ and } (260)/(3)` respectively.