seven times the sum of a number and seven is 13 more than the number. what is the number?
i know it cant be that hard but please help
yes! thank you much
Let's break down the problem step-by-step:
Let's assign a variable to the unknown number. Let's call it "x".
"Seven times the sum of a number and seven" can be written as 7(x + 7).
"Is" implies "equals", so we can set up an equation:
7(x + 7) = x + 13
Now, we can solve the equation:
7x + 49 = x + 13
Simplify the equation by subtracting x from both sides:
7x - x + 49 = 13
Combining like terms:
6x + 49 = 13
Subtract 49 from both sides:
6x = 13 - 49
Simplifying:
6x = -36
Divide both sides by 6:
x = -36 / 6
Simplifying:
x = -6
Therefore, the number is -6.
To find the number, let's break down the information given in the question.
Let's assume that the number is represented by "x".
The sentence "seven times the sum of a number and seven" can be translated into an equation as follows: 7(x + 7).
The sentence "is 13 more than the number" can be translated into an equation as follows: x + 13.
Now, let's combine these two equations to represent the given information:
7(x + 7) = x + 13
To solve for x, we need to simplify and solve the equation:
7x + 49 = x + 13
To isolate x, we need to move all terms containing x to one side of the equation:
7x - x = 13 - 49
6x = -36
To solve for x, we divide both sides of the equation by 6:
x = -36 / 6
x = -6
Therefore, the number is -6.
7(x+7)=x+13
7x+49=x+13
7x-x+49=x-x+13
6x+49=13
6x+49-49=13-49
6x=-36
(6x)/6=(-36)/6
x=-6
Is that what you were looking for?