There are 45 pounds and 30 pounds of each type respectively.
Step-by-step explanation:
Since we have given that
Cost of first type = $2 per pound
Cost of second type = $7 per pound
Cost of mixture = $4 per pound
So, we need to find the quantity of each type to make 75 pounds of a blend.
We will use "Mixture and Allegations":
First type Second type
2 7
4
---------------------------------------------------
7 - 4 : 4 - 2
3 : 2
So, Quantity of first type would be
![\dfrac{3}{5}\times 75=3\times 15=45\ pounds](https://tex.z-dn.net/?f=%5Cdfrac%7B3%7D%7B5%7D%5Ctimes%2075%3D3%5Ctimes%2015%3D45%5C%20pounds)
Quantity of second type would be
![\dfrac{2}{5}\times 75=2\times 15=30\ pounds](https://tex.z-dn.net/?f=%5Cdfrac%7B2%7D%7B5%7D%5Ctimes%2075%3D2%5Ctimes%2015%3D30%5C%20pounds)
Hence, there are 45 pounds and 30 pounds of each type respectively.