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 the steps
$34 + 12w ≥ 205
Subtract 34 from both sides:
12w ≥ 171
Divide both sides by 12:
w ≥ 14.25
Since Anna must save for a whole number of weeks, the minimum number of weeks it will take Anna to save the money to purchase the bike is 15 weeks.
To find the minimum number of weeks it will take Anna to save the money to purchase the bike, we can use the following inequality:
Savings per week * Number of weeks ≥ Cost of the bike - Saved amount
Let's plug in the values given in the problem:
$12 * w ≥ $205 - $34
Simplifying the equation further:
$12w ≥ $171
Now we can solve for w by dividing both sides of the equation by $12 to isolate w:
w ≥ $171/$12
w ≥ 14.25
Since we can't have a fraction for the number of weeks, we round up to the next whole number. Therefore, the minimum number of weeks it will take Anna to save enough money to purchase the bike is 15 weeks.
To find the minimum number of weeks, w, it will take Anna to save enough money to purchase the bike, we can use the following inequality:
204 - 34 ≤ 12w
To obtain this inequality, we subtract the amount Anna has already saved, which is $34, from the cost of the bike, which is $205, and set it less than or equal to the weekly saving rate, which is $12, multiplied by the number of weeks, w.
Simplifying the inequality:
170 ≤ 12w
Next, we can divide both sides of the inequality by 12 to solve for w:
170/12 ≤ w
Which can be further simplified:
14.167 ≤ w
Since the number of weeks must be a whole number, we round up to the next whole number to find the minimum number of weeks it will take Anna to save the money:
w ≥ 15
Therefore, it will take Anna a minimum of 15 weeks to save enough money to purchase the bike.