8 (n + 6) = 104 identify8 (n + 6) = 104 identify the real world problem that corresponds to this equation
A real-world problem that corresponds to the equation 8(n + 6) = 104 could be calculating the total cost of purchasing a certain number of items.
Suppose you want to buy n items, and each item costs $8. Additionally, there is a special promotion where if you buy 6 or more items, you get a $104 discount. The equation represents the total cost of buying n items, with the additional discount if applicable.
By simplifying the equation, you can find the value of n and determine how many items you need to buy in order to receive the discount.
The real-world problem that corresponds to the equation 8(n + 6) = 104 could be calculating the cost of purchasing a certain number of items with a discount applied. Let's break it down step-by-step:
Step 1: Write the equation
8(n + 6) = 104
Step 2: Simplify the equation
Distribute 8 to both terms inside the parentheses:
8n + 48 = 104
Step 3: Isolate the variable
Subtract 48 from both sides of the equation to isolate the variable:
8n = 104 - 48
8n = 56
Step 4: Solve for the variable
Divide both sides of the equation by 8 to solve for n:
n = 56/8
n = 7
In this case, the equation is used to determine the value of n (the number of items) in a situation where each item costs 8 units (dollars, for example) and there is a discount of 6 units. The equation states that the total cost (price) of the items is equal to 104 units.
To identify the real-world problem that corresponds to the equation 8(n + 6) = 104, we need to analyze what the equation is representing.
The equation can be simplified by using the distributive property, which states that multiplying a number outside the parentheses to the terms inside the parentheses.
Let's solve the equation step by step:
8(n + 6) = 104
First, we distribute 8 to each term inside the parentheses:
8n + 48 = 104
Next, we isolate the term with the variable, n, by subtracting 48 from both sides of the equation:
8n + 48 - 48 = 104 - 48
This simplifies to:
8n = 56
Finally, we isolate the variable, n, by dividing both sides of the equation by 8:
(8n)/8 = 56/8
This yields:
n = 7
Now, let's see how this equation can be related to a real-world problem.
Suppose there is a situation where you have a certain number, n, and you want to find out what number multiplied by 8, then added to 48, will result in a sum of 104.
In this case, the real-world problem could be finding the value of n, which represents the unknown number, that satisfies the equation.
For example, if you have a certain quantity of something, represented by n, and you want to determine how many times it needs to be multiplied by 8, then when you add 48, you will end up with a total of 104. The value of n in this situation would be 7.
So, a possible real-world problem that corresponds to this equation could be finding the original quantity (n) based on a specific multiplication and addition condition.