Sales of products

For 80 pieces of two quality products a total sales is 175 Eur. If the first quality product was sold for n EUR per piece (n natural number) and the second quality product after 2 EUR per piece. How many pieces of the first quality were sold?

Result

a1 =  15
a2 =  5
a3 =  3
a4 =  1

Solution:

a+b=80 n a+2b=175 n a+2 (80a)=175 n a+1602 a=175 a(n2)=15 n1=3 a1=15/(n12)=15/(32)=15a+b = 80 \ \\ n \cdot \ a+2b = 175 \ \\ n \cdot \ a + 2 \cdot \ (80-a) = 175 \ \\ n \cdot \ a + 160 - 2 \cdot \ a = 175 \ \\ a(n-2) = 15 \ \\ n_{ 1 } = 3 \ \\ a_{ 1 } = 15 / (n_{ 1 }-2) = 15 / (3-2) = 15
n2=5 a2=15/(n22)=15/(52)=5n_{ 2 } = 5 \ \\ a_{ 2 } = 15 / (n_{ 2 }-2) = 15 / (5-2) = 5
n3=7 a3=15/(n32)=15/(72)=3n_{ 3 } = 7 \ \\ a_{ 3 } = 15 / (n_{ 3 }-2) = 15 / (7-2) = 3
n4=17 a4=15/(n42)=15/(172)=1n_{ 4 } = 17 \ \\ a_{ 4 } = 15 / (n_{ 4 }-2) = 15 / (17-2) = 1



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