# 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:

$a+b = 80 \ \\ n \cdot \ a+2b = 175 \ \\ n \cdot \ a + 2 \cdot \ (80-a) = 175 \ \\ n \cdot \ a + 160 - 2 \cdot \ a = 175 \ \\ a(n-2) = 15 \ \\ n_{ 1 } = 3 \ \\ a_{ 1 } = 15 / (n_{ 1 }-2) = 15 / (3-2) = 15$
$n_{ 2 } = 5 \ \\ a_{ 2 } = 15 / (n_{ 2 }-2) = 15 / (5-2) = 5$
$n_{ 3 } = 7 \ \\ a_{ 3 } = 15 / (n_{ 3 }-2) = 15 / (7-2) = 3$
$n_{ 4 } = 17 \ \\ a_{ 4 } = 15 / (n_{ 4 }-2) = 15 / (17-2) = 1$ Our examples were largely sent or created by pupils and students themselves. Therefore, we would be pleased if you could send us any errors you found, spelling mistakes, or rephasing the example. Thank you!

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