Question

The Comfort Coffee Company wants to mix 3030 pounds of their Smooth blend worth $ 5$5 a pound with their Special blend worth $ 7$7 a pound in order to create a new blend of coffee worth $ 5.50$5.50 a pound. How many pounds of the Special blend should be added to the Smooth​ blend?

Answer 1

Answer:

10 pounds of Special blend coffee needs to be added to create to new blend of coffee.

Step-by-step explanation:

Given:

Amount of Smooth blend coffee = 30 pounds

Cost of Smooth blend coffee each pound = $5

Cost of Special Blend coffee each pound = $7

Cost of New mix coffee each pound= $5.5

We need to find the Amount Special Blend to be added.

Solution:

Let the Amount Special Blend to be added be 'x'.

Total Cost of Smooth blend coffee will be Amount of Smooth blend coffee multiplied by Cost of Smooth blend coffee each pound.

framing in equation form we get;

Total Cost of Smooth blend coffee = $30\times5 =150$

Now we can say that;

Total Cost of Special Blend coffee is equal to Cost of Special Blend coffee each pound multiplied by the Amount Special Blend to be added.

Total Cost of Special Blend coffee = $7\times x =7x$

Now Total Amount of Coffee to make the mixture is equal to sum of Amount of Smooth blend coffee and Amount Special Blend to be added.

framing in equation form;

Total Amount of Coffee to make the mixture = $30+x$

Now we can say that;

Cost of New mix coffee each pound will be equal to sum of Total Cost of Special Blend coffee and Total Cost of Smooth blend coffee divided by Total Amount of Coffee to make the mixture.

framing in equation form we get;

$\frac{150+7x}{30+x}=5.5$

By Using Cross multiplication we get;

$150+7x=5.5(30+x)$

Applying Distributive property we get;

$150+7x=165+5.5x$

Combining the like terms we get;

$7x-5.5x=165-150\\\\1.5x=15$

Dividing both side by 1.5 we get;

$\frac{1.5x}{1.5}=\frac{15}{1.5}\\\\x=10\ pounds$

Hence 10 pounds of Special blend coffee needs to be added to create to new blend of coffee.