Answer:
C
Explanation:
Let p represent the cost for one pound of peanuts and let c represent the cost for one pound of cashews.
Two pounds of peanuts and three pounds of cashews cost $17.50. So:
![2p+3c=17.5](https://img.qammunity.org/2022/formulas/mathematics/high-school/f3rv2lmu37txzs99dbywcdy018zo84pgd6.png)
Five pounds of peanuts and two pounds of cashews cost $19.00. So:
![5p+2c=19](https://img.qammunity.org/2022/formulas/mathematics/high-school/3ue43h5o81jtpromoqne5c3apbbdz2d4ab.png)
This yields a system of equations.
We can solve this using elimination. We can multiply the first equation by -5, and the second by 2. Therefore:
![-5(2p+3c)=-5(17.5)](https://img.qammunity.org/2022/formulas/mathematics/high-school/in71sfm5tsahau61col2jm0c5dwuzod90g.png)
Multiply:
![-10p-15c=-87.5](https://img.qammunity.org/2022/formulas/mathematics/high-school/gophpf8g2npqkl7tzxu48nn1b9a68yr31w.png)
And:
![2(5p+2c)=2(19)](https://img.qammunity.org/2022/formulas/mathematics/high-school/jyj5ue763o2s8sguelk6oza8vfl0edmey5.png)
Multiply:
![10p+4c=38](https://img.qammunity.org/2022/formulas/mathematics/high-school/jamz3pykjfovtsm5qnpwzkvz8fuknzm8lz.png)
Now, we can add the two equations together:
![(-10p-15c)+(10p+4c)=(-87.5+38)](https://img.qammunity.org/2022/formulas/mathematics/high-school/9g7lixyp5pjyyrhy24qpxtm6376q9mv95u.png)
Combine like terms:
![-11c=-49.5](https://img.qammunity.org/2022/formulas/mathematics/high-school/6xet1bf8rrtpzsstzt8kal83sxjs2zg3uf.png)
Therefore:
![c=4.5](https://img.qammunity.org/2022/formulas/mathematics/high-school/pveelp7vq7tuq5bqaekdsfw290379s3k7d.png)
So, a pound of cashews costs $4.50.
Our answer is C.
Notes:
To solve for the cost for peanuts, we can use the first (or second equation) again:
![2p+3c=17.5](https://img.qammunity.org/2022/formulas/mathematics/high-school/f3rv2lmu37txzs99dbywcdy018zo84pgd6.png)
Substitute:
![2p+3(4.5)=17.5](https://img.qammunity.org/2022/formulas/mathematics/high-school/a0ydnzn7hpczc4qqbz1vulqaptl5sfcraj.png)
Solve for p:
![2p+13.5=17.5\Rightarrow 2p=4\Rightarrow p=2](https://img.qammunity.org/2022/formulas/mathematics/high-school/y2o8qmr9yj69tsj6ukavcs8nfyudb967mh.png)
So, a pound of peanutes cost $2.00.