# 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:

$a+b=80 \ \\ n \cdot \ a+2b=175 \ \\ n \cdot \ a + 2 \cdot \ (80-a)=175 \ \\ n \cdot \ a + 160 - 2 \cdot \ a=175 \ \\ a(n-2)=15 \ \\ n_{1}=3 \ \\ a_{1}=15 / (n_{1}-2)=15 / (3-2)=15$
$n_{2}=5 \ \\ a_{2}=15 / (n_{2}-2)=15 / (5-2)=5$
$n_{3}=7 \ \\ a_{3}=15 / (n_{3}-2)=15 / (7-2)=3$
$n_{4}=17 \ \\ a_{4}=15 / (n_{4}-2)=15 / (17-2)=1$

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