Final answer:
Sarah needs to save money for a bicycle and saves $10 each week. An equation models her savings over time. By solving the equation, we find that she has to save for 7 weeks to afford the bike.
Step-by-step explanation:
Imagine Sarah is saving money for a new bicycle. She already has $30 saved and is able to save an additional $10 each week. After 5 weeks, she finds a bike on sale for $100. We can represent her total savings with the equation S = 10w + 30, where S is the total money saved, and w is the number of weeks she saves. To find out if she has enough to buy the bike after 5 weeks, we substitute w with 5 to get S = 10(5) + 30, which simplifies to S = 50 + 30 or S = 80. This means Sarah is $20 short of the sale price of the bike.
To determine how many more weeks she needs to save to have enough for the bike, we can use another equation with her total savings goal: 100 = 10w + 30. Subtract 30 from both sides to get 70 = 10w, then divide both sides by 10 to find w = 7. Sarah needs to save for 7 weeks in total to buy her bicycle.