Write a real-life situation to fit the following equation. Then, solve the equation in two different ways. Show all the steps. Finally, choose which solution method you liked best and explain your reason.
8(x+9)=144
Real-life situation:
Let's say you are shopping at a store where every item costs the same amount. You want to buy 8 items, and they are each priced at "x" dollars. However, the store is having a sale where if you buy 9 items, you get a 10% discount on your total purchase. You want to find the value of "x" so that the total cost of buying 8 items will be equal to $144 after the discount is applied.
Solution Method 1: Distributive Property and Simple Algebra
Step 1: Apply the distributive property by multiplying 8 by the terms inside the parentheses.
8(x + 9) = 144
8x + 72 = 144
Step 2: Simplify the equation by subtracting 72 from both sides to isolate the variable.
8x = 144 - 72
8x = 72
Step 3: Solve for x by dividing both sides by 8.
x = 72/8
x = 9
Solution Method 2: Reasoning and Division
Step 1: Divide the total cost, $144, by the number of items being purchased, 8, to find the price per item.
144 ÷ 8 = 18
Step 2: Since buying 9 items qualifies for a discount, we can assume that the original price per item, without the discount, was 10% higher than the discounted price. So, the original price per item is:
18 ÷ 0.9 = 20
Step 3: Subtract 9 from the original price per item (since we are buying 8 items instead of 9) to find the value of x.
20 - 9 = 11
Solution:
Both solution methods give us the same result: x = 9.
Personally, I prefer Solution Method 2 (Reasoning and Division) because it provides a bit more context and reasoning behind the calculations. It allows you to think through the problem logically and understand the relationship between the discounted price, the original price, and the number of items being purchased. However, Solution Method 1 (Distributive Property and Simple Algebra) is also valid, especially when dealing with more complex equations.