Question

Hong's Coffee Shop makes a blend that is a mixture of two types of coffee. Type A coffee costs Hong $4.25 per pound, andtype B coffee costs $5.40 per pound. This month, Hong made 160 pounds of the blend, for a total cost of $765.10. Howmany pounds of type A coffee did he use?

Answer 1

1) Gathering the data

A =$4.25

B =$5.40

160 lb

Total Costa: $ 765.10

2) In this question, we can set a pair of Linear equations and then solve it to get how many pounds for A, and B. So we can write out:

4.25a +5.40b =765.10 This equation relates the cost

a + b = 160 And this one relates the quantity

We can solve this using the Elimination Method, multiplying the whole 2nd equation by -5.40 to add them and eliminate b:

4.25a + 5.40b = 765.10

a + b = 160 x(-5.40)

4.25a + 5.40b = 765.10

-5.4a -5.4b = -864

-------------------------------------------

-1.15a = -98.9 Divide both sides by -1.15

a = 86

b = 160 -86, b =74

3) Since the question is only about A, then the answer is 86 pounds of coffee