The sum of 3 numbers is 67. Second number is 2 times the third. The first number is 7 more than the 3rd. What are the numbers?

Question

The sum of 3 numbers is 67. Second number is 2 times the third. The first number is 7 more than the 3rd. What are the numbers?

Answer 1

Let's represent the problem with algebraic expressions:

x + y + z = 67

y = 2z

x = z + 7

So we can rewrite the expression in terms in z with one unknown and find the three numbers:

x + y + z = 67

(z + 7) + (2z) + z = 67

4z + 7 = 67

4z = 60

z = 15

If z = 15 then x = z + 7 = 15 + 7 = 22 and y = 2z = 2 * 15 = 30

x = 22, y = 30, z =15

Answer 2

Hello Leanah,

Let the following expressions represent each number:

First number = x + 7

Second number = 2x

Third number = x

Now, we add all of the above terms or expressions together and set the equation equal to 67.

Therefore:

x + 7 + 2x + x = 67 <----combine like terms

4x + 7 = 67 <----subtract 7 from both sides

4x = 60 <----divide both sides by 4

x = 15 <----this is the third number

2x = 30 <----this is the second number

x + 7 = 22 <----this is the first number

Now, let's check our work, okay? Do the three numbers equal 67?

15 + 30 + 22 = 67

67 = 67

Yes, the solution checks out.

I hope this assists and that you have a great rest of the week. If you have any feedback or further questions regarding this solution, please leave it or them, in a comment beneath the solution. If you need further assistance, please feel free to reach out to any tutor. Best!

Answer 3

Hi, Leanah.

X + Y + Z = 67

Y = 2Z

X = 7 + Z

Now, substitute:

7 + Z + 2Z + Z = 67

4Z = 60

Z = 15

Y = 2Z = 30

X = 7 + Z = 22

The numbers are:

22, 30, 15

Answer 4

Hi, Leanah.

X + Y + Z = 67

Y = 2Z

X = 7 + Z

Now, substitute:

7 + Z + 2Z + Z = 67

4Z = 60

Z = 15

Y = 2Z = 30

X = 7 + Z = 22

The numbers are:

22, 30, 15

Answer 5

first number = x

second number = y

third number = z

x+y+z = 67 ---------- eq 1

y =2z

x =z+7

now substituting value of y and z in equation 1

z+7 +2z +z =67

4z =60

z = 15

y=2(15)=30

x=15+7=22

Answer 6

first number = x

second number = y

third number = z

x+y+z = 67 ---------- eq 1

y =2z

x =z+7

now substituting value of y and z in equation 1

z+7 +2z +z =67

4z =60

z = 15

y=2(15)=30

x=15+7=22