Question

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

Also, she saved 34 Dollars, not 31, I'm repeating this because I'm getting answers that are incorrect because of this error

Answer 1

w>14.25

Explanation:

Answer 2

w ≥ 14.25

Explanation:

You want to solve the inequality 34 +12w ≥ 205 for the number of weeks (w) Anna will take to save for a new bike.

Solution

This is a 2-step inequality.

Step 1: subtract the constant from both sides:

34 -34 +12w ≥ 205 -34

12w ≥ 171

Step 2: divide by the coefficient of the variable

12w/12 ≥ 171/12

w ≥ 14.25

It will take Anna a minimum of 14.25 weeks to save the money to purchase the bike.

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Additional comment

Often, income does not come as a continuous stream, so 14.25 weeks would mean 15 weeks at a minimum.

If Anna earns the last $3 she needs in 1/4 week, then 14 1/4 weeks is the right answer.

This has to do with the practical domain of w in this problem. If w is restricted to integers, then w ≥ 15. Regardless, the answer needs to be given in a way that will satisfy your answer checker.

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