Question

A store is having a sale on walnuts and chocolate chips . For 3 pounds of walnuts and 2 pounds chocolate Chips,the cost is $12. For 5 pounds of walnuts and 6 pounds of chocolate chips the total cost is $30. Find the cost for each pound of walnuts and each pound of chocolate chips

Answer 1

Cost of one pound of walnuts = x = $1.5

Cost of one pound of Chocolate chip = y =$3.75

Explanation:

Let:

Cost of one pound of walnuts = x

Cost of one pound of Chocolate chip = y

Now making equations from the statements.

For 3 pounds of walnuts and 2 pounds chocolate Chips,the cost is $12:
`3x+2y=12`

For 5 pounds of walnuts and 6 pounds of chocolate chips the total cost is $30:
`5x+6y=30`

We need to solve these equations to find values of x and y

Let:

`3x+2y=12--eq(1)\\5x+6y=30--eq(2)`

Multiply eq(1) by 3 and subtract both equations

`9x+6y=36\\5x+6y=30\\- \ \ \ - \ \ \ \ -\\-------\\4x=6\\x=(6)/(4)\\x=1.5`

Now, finding value of y bu putting value of x, x= 1.5 in eq(1)

`3x+2y=12\\3(1.5)+2y=12\\4.5+2y=12\\2y=12-4.5\\2y=7.5\\y=(7.5)/(2)\\y=3.75`

So, we get value of y: y=3.75

Cost of one pound of walnuts = x = $1.5

Cost of one pound of Chocolate chip = y =$3.75