Anna would like to purchase a new bike that cost $205. She already has saved $34. If she saves a maximum of $12 a week, the following inequality can be used to find the minimum number of weeks, w, it will take Anna to save the money to purchase the bike Please show steps
I need the steps for all five questions
12w + 34 ≥ 205
12w ≥ 171
w ≥ 14.25
Therefore, it will take Anna at least 15 weeks to save the money to purchase the bike.
Sure! Let's go through each question step by step:
Question 1: What's the inequality that can be used to find the minimum number of weeks, w, it will take Anna to save the money?
To determine the minimum number of weeks Anna needs to save in order to purchase the bike, we can use the inequality:
34 + 12w >= 205
This inequality states that the money Anna has already saved, 34 dollars, plus the amount she saves each week, 12 dollars multiplied by the number of weeks (w), should be greater than or equal to the cost of the bike, 205 dollars.
Question 2: Anna wants to purchase a bike that costs $205. How much money has she saved already?
According to the question, Anna has saved 34 dollars already.
Question 3: How much money can Anna save each week?
According to the question, Anna can save a maximum of 12 dollars per week.
Question 4: What is the cost of the bike that Anna wants to purchase?
According to the question, the bike costs 205 dollars.
Question 5: Solve the inequality to find the minimum number of weeks, w.
To solve the inequality, we need to isolate the variable w to determine the minimum number of weeks Anna needs to save. Here are the steps:
1. Subtract 34 from both sides of the inequality to isolate the term with w:
12w >= 205 - 34
12w >= 171
2. Divide both sides of the inequality by 12 to solve for w:
w >= 171/12
3. Simplify:
w >= 14.25
Therefore, the minimum number of weeks, w, Anna needs to save to purchase the bike is 14.25 weeks. However, since weeks cannot be fractional, Anna would need to save for at least 15 weeks.
To find the minimum number of weeks it will take Anna to save enough money to purchase the bike, we can use the following inequality:
34 + 12w ≥ 205
Step 1: Subtract 34 from both sides of the inequality to isolate the term with the variable, w:
12w ≥ 205 - 34
12w ≥ 171
Step 2: Divide both sides of the inequality by 12 to solve for w:
w ≥ 171 ÷ 12
w ≥ 14.25
Since w represents the number of weeks, it cannot be a decimal or fraction. Therefore, we must round up the value to the next whole number:
w ≥ 15
Thus, it will take Anna a minimum of 15 weeks to save enough money to purchase the bike.