Volunteers 81981

Volunteers planted saplings in the forest nursery; spruces made up 55% of all saplings; one-third were edible, and the rest were young pines. How many saplings did they plant if the number of saplings was greater than 1060 and less than 1090?

Correct answer:

n =  1080

Step-by-step explanation:

$$\begin{gathered} r_1=55\%=\frac{55}{100}=\frac{11}{20}=0.55 \\ {r}_2=1/3=\frac{1}{3}\doteq 0.3333 \\ {r}_3=1-r_1-r_2=1-0.55-0.3333=\frac{7}{60}\doteq 0.1167 \\ {d}_1=1060/60=\frac{53}{3}=17\frac{2}{3}\doteq 17.6667 \\ {d}_2=1090/60=\frac{109}{6}=18\frac{1}{6}\doteq 18.1667 \\ d=\lfloor d_2\rfloor =\lfloor 18.1667\rfloor =18 \\ n=d\cdot 60=18\cdot 60=1080 \\ \text{ Verifying Solution: } \\ a=r_1\cdot n=0.55\cdot 1080=594 \\ b=r_2\cdot n=0.3333\cdot 1080=360 \\ c=r_3\cdot n=0.1167\cdot 1080=126 \\ N=a+b+c=594+360+126=1080 \end{gathered}$$

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