Find four consecutive odd numbers which add to 64.
Let the first number be x. The next three numbers are:
x + 2
x + 4
x + 6
Add them together to get 64:
x + (x + 2) + (x + 4) + (x + 6) = 64
Group like terms:
4x + 12 = 64
Using our equation calculator, we get:
x = 13
The next 3 odd numbers...
Two consecutive even integers that equal 126
Let the first integer equal x. So the next even integer must be x + 2.
The sum which is equal to 126 is written as x + (x + 2) = 126
Simplify:
2x + 2 = 126
Using our equation calculator, we get:
x = 62
This means the next consecutive even integer...
To make an international telephone call, you need the code for the country you are calling. The code for country A, country B, and C are three consecutive integers whose sum is 90. Find the code for each country.
If they are three consecutive integers, then we have:
B = A + 1
C = B + 1, which...
The square of a positive integer minus twice its consecutive integer is equal to 22. Find the integers.
Let x = the original positive integer. We have:
Consecutive integer is x + 1
x^2 - 2(x + 1) = 22
Multiply through:
x^2 - 2x - 2 = 22
Subtract 22 from each side:
x^2 - 2x - 24 = 0
Using...
Find 3 Even Integers with a sum of 198
Let x be the first even integer. Then y is the next, and z is the third even integer.
y = x + 2
z = x + 4
x + y + z = 198
Substituting y and z into (3):
x + x + 2 + x + 4 = 198
Group x terms
3x + 6 = 198
Using our equation solver, we...
There are 2 consecutive integers. Twice the first increased by the second yields 16. What are the numbers?
Let x be the first integer. y = x + 1 is the next integer. We have the following givens:
2x + y = 16
y = x + 1
Substitute (2) into (1)
2x + (x + 1) = 16
Combine x terms
3x + 1 = 16...
Let x be the first even integer. That means the next consecutive even integer must be x + 2.
Set up our equation:
x + (x + 2) = 118
Group x terms
2x + 2 = 118
Subtract 2 from each side
2x = 116
Divide each side by 2
x = 58
Which means the next consecutive even integer is 58 + 2 = 60
So...
Let the 3 integers be x, y, and z.
y = x + 1
z = y + 1, or x + 2.
Set up our equation:
x + (x + 1) + (x + 2) = 42
Group our variables and constants:
(x + x + x) + (1 + 2) = 42
3x + 3 = 42
Subtract 3 from each side:
3x = 39
Divide each side of the equation by 3:
x = 13
So y = x + 1 = 14
z =...
A set of 4 consecutive integers adds up to 314. What is the least of the 4 integers?
First integer is x. The next 3 are x + 1, x + 2, and x + 3. Set up our equation:
x + (x + 1) + (x + 2) + (x + 3) = 314
Group x terms and group constnats
(x + x + x + x) + (1 + 2 + 3) = 314
Simplify and...
So x + y <=18
y = x + 1
x + x + 1 <=18
2x + 1 <= 18
Subtract 1 from both sides
2x <= 17
x<=8.5 --> 8
So we have {(0,1),(1,2),(2,3),(3,4),(4,5),(5,6),(6,7),(7,8),(8,9)}