blank CDs come in spindles of 25 or 60. Rachel needs 230 blank CDs for her eighth grade science class. how many spindles of each amount should she buy?

Hello!The answer is:She needs to buy 3 spindles of 60 CDS and 2 spindles of 25 CDs.Why?We know that the possibilities will depend always on how many CDs contain each type of spindles.There is only one possible combination of spindles that can give the exact amount of CDs needed.Let's try to find the combinations:- First combination: With 1 spindle of 60 CDs:[tex]Spindles_{25}=\frac{TotalCDs-NoOfSpindles_{60}}{25} \\\\Spindles_{25}=\frac{230-60}{25}=\frac{170}{25}=6.8Spindles[/tex]Since the result is not a whole number, we know that the first combination does not work.- Second combination: With 2 spindles of 60 CDs:[tex]Spindles_{25}=\frac{TotalCDs-NoOfSpindles_{60}}{25} \\\\Spindles_{25}=\frac{230-(2)*60}{25}=\frac{110}{25}=4.4Spindles[/tex]Since the result is not a whole number, we know that the second combination does not work.- Third combination: With 3 spindles of 60 CDs:[tex]Spindles_{25}=\frac{TotalCDs-NoOfSpindles_{60}}{25} \\\\Spindles_{25}=\frac{230-(3)*60}{25}=\frac{230-180}=\frac{50}{25}=2Spindles[/tex]Since the result is a whole number, we know that the third combination works.Hence, the combination will be:[tex]TotalCDs=3Spindles_{60}+2Spindles_{25}=3*60+2*25=180+50=230[/tex]She needs to buy 3 spindles of 60 CDs and 2 spindles of 25 CDs.Have a nice day!