tia plays the guitar. she usually buys guitar strings for $12. she has to buy new strings every 4 weeks. now…

tia plays the guitar. she usually buys guitar strings for $12. she has to buy new strings every 4 weeks. now tia is buying better guitar strings for $33. tia was told they last a lot longer. how long do the new strings need to last to get at least equal value per week? 8 weeks 9 weeks 11 weeks 12 weeks

tia plays the guitar. she usually buys guitar strings for $12. she has to buy new strings every 4 weeks. now tia is buying better guitar strings for $33. tia was told they last a lot longer. how long do the new strings need to last to get at least equal value per week? 8 weeks 9 weeks 11 weeks 12 weeks

Answer

Explanation:

Step1: Calculate cost - per - week of old strings

The old strings cost $12 and last 4 weeks. The cost - per - week of old strings is $\frac{12}{4}=3$ dollars per week.

Step2: Set up an equation for new strings

Let the number of weeks the new strings last be $x$. The new strings cost $33$. We want the cost - per - week of new strings to be at most 3 dollars (the same as the old strings). So, the cost - per - week of new strings is $\frac{33}{x}$, and we set up the inequality $\frac{33}{x}\leq3$.

Step3: Solve the inequality

Multiply both sides of the inequality $\frac{33}{x}\leq3$ by $x$ (assuming $x>0$). We get $33\leq3x$. Then divide both sides by 3: $x\geq11$.

Answer:

11 weeks