My Scenario:
I want to buy a gaming laptop that costs $1,200. I currently have $400 saved, and I save $100 each month. How many months will it take for me to afford the laptop?
Post 1 Response:
In the scenario of purchasing a truck:
-
Equation: To find out how many weeks (\( w \)) it will take to save for the truck:
\[ 500 + 250w = 9000 \] Subtracting 500 from both sides:
\[ 250w = 8500
\]
Dividing by 250:
\[ w = 34 \] -
Inequality: To determine how many weeks it takes for the amount saved to be at least $9,000:
\[ 500 + 250w \geq 9000 \]
Solving it leads to:
\[ 250w \geq 8500 \implies w \geq 34 \]
Explanation: The equation gives the exact number of weeks needed to reach exactly $9,000, which is 34 weeks, while the inequality shows that at least 34 weeks are necessary to meet or exceed that amount. Both express the same concept but in different terms — the equation for a precise answer and the inequality for a range of feasible timeframes.
Post 2 Response:
In the scenario of saving for a fishing rod and reel:
-
Equation: To determine if savings over 10 weeks can meet the total cost of $500:
\[ 100 + 50w = 500 \]
Subtracting 100 from both sides:
\[ 50w = 400
\]
Dividing by 50:
\[ w = 8 \] -
Inequality: To check if it will take more than 10 weeks to save up:
\[ 100 + 50w < 500 \]
Subtracting 100 gives:
\[ 50w < 400 \implies w < 8 \]
Explanation: The equation tells us that exactly 8 weeks will allow for the purchase of both items, while the inequality shows that if I only save for 10 weeks, I will have saved too much, which reflects that the savings goal can indeed be met in less than the 10-week threshold. Thus, the inequality confirms that I will achieve my goal in less time than expected.