Money - Ratio Problem (Please Explain Too)

Question

Kelly blends coffee. She mixes brand A costing $6 per kilogram with brand B costing $8 per kilogram. How many kilograms of each brand does she have to mix to make 50 kg of coffee costing her $7:20 per kg?

Answer 1

Hi David! 

 

You can solve this kind of problem with a system of linear equations.

 

x = kg of brand A

y = kg of brand B

 

We know the total weight of the mix is 50 kg, so:

x+y = 50

 

We know how much each kg costs and what the total cost is, so:

6x + 8y = 7.2(50)

 

If you don't have a graphing calculator, substitution is an easy way to solve this.

x+y = 50

y = 50 - x

 

6x +8y = 7.2(50)

6x +8(50-x)=360

6x-8x + 400 = 360

-2x = -40

 

x = 20

Since x + y = 50, we also know that y = 30.

 

Check your solution:

20(6) + 30(8) = 7.2(50)

 

360 = 360

 

Brand A: 20 kg

Brand B: 30 kg

 

Let me know if you have questions! :)