How many pounds of type A coffee were used ?

Question

Kiras Coffee Shop makes a blend that is a mixture of two types of coffee. Type A coffee costs Kira $4.30 per pound, and type B coffee costs $5.50 per pound. This months blend used four times as many pounds of type B coffee as type A, for a total cost of $789.00. How many pounds of type A coffee were used ?

Answer 1

For this type of question, it is important to first figure out what the problem is asking you to find -- often, that is going to be your variable.  In this question, they want to know how many pounds of type A coffee were used.  Let's use that as our variable:

 

Let x = the number of pounds of type A coffee used

 

Next, let's pull out the other information the problem gives us:

 

Cost per pound of type A coffee = $4.30/lb

Cost per pound of type B coffee = $5.50/lb

 

This month, the blend used four times as many pounds of type B coffee as type A.

So,the number of pounds of type B coffee used = 4(number of pounds of type A coffee used) = 4x

 

The total cost for this month's blend was $789.00.

 

Next, let's put this information together.

 

The total cost of type A coffee = (cost per pound of type A coffee)*(number of pounds of type A coffee) = ($4.30)*(x) = 4.3x

 

The total cost of type B coffee = (cost per pound of type B coffee)*(number of pounds of type B coffee) = ($5.50)*(4x) = (5.5)*(4x) = 22x

 

The total cost of this month's blend = total cost of type A coffee + total cost of type B coffee

789.00 = 4.3x + 22x

789 = 26.3x

30 = x

 

Don't just circle x = 30!  Remember to answer the question being asked!  In this case, the answer would be that 30 pounds of type A coffee were used to make this month's blend.

Answer 2

Hi Arianna,

We know 4A=B (because 4x as many pounds of B were used as A)

So 4.30A + 5.50(4A) = 789.00

Solve for A.