Find how much high quality coffee bean and how much cheaper coffee bean she should blend

Question

Sarah needs to prepare 140 pounds of blended coffee beans selling for $4.45 per pound. She plans to do this by blending together a high quality bean costing $5.25 per pound and a cheaper bean at $3.00 per pound. To the nearest pound find how much high quality coffee bean and how much cheaper coffe bean she should blend.

Answer 1

Let H= pounds of high quality coffee beans

so 140-H is the number of pounds of the cheaper beans

The mixture will contain H pounds at 5.25/pound and

140-H pounds at 3.00/ pound

So 5.25H + 3(140-H) = 140 pounds at 4.45/pound

5.25H + 420 -3H = 623

2.25H = 203

H= 90.22. So nearest number of pounds of H (high quality beans) is 90 and 50 pounds of the cheaper beans

Answer 2

I worked out the problem and got a fraction answer so I wonder if all the numbers are shown correctly

x = amount at $5.25

y = amount at $3.00

x + y = 140 pounds

The total cost of the blend will be 140 x $4.45 and that equals $623

The cost of the expensive beans will be 5.25x

The cost of the cheaper beans will be 3.00y

5.25x + 3.00y = 623

solve the first equation for y

y = 140 - x

substitute into the 2nd equation

5.25x + 3.00(140 - x) = 623

5.25 x + 420 - 3.00 x = 623

2.25 x = 203

x = 90 2/9

y = 140 - 90 2/9

y = 49 7/9

Use 90 2/9 of the 5.25 bean and

49 7/9 of the 3.00 bean

Watch for other answers to verify the above solution