Need help on solving word problems

Question

Sarah Meeham blends coffee for Tasti-Delight. She needs to prepare 160 pounds of blended coffee beans selling for $4.50 per pound. She plans to do this by blending together a high-quality bean costing $5.25 per pound and a cheaper bean at $3.25per pound. To the nearest pound, find how much high-quality coffee bean and how much cheaper coffee bean she should blend.

She should blend ___ many pounds of high quality beans.

She should blend ___ many pounds of cheaper beans.

Answer 1

Kozie picked 52 more mushrooms than alex. On the way home, Kozie gave 28 mushrooms to Alex. Now who has more mushrooms and how much more?

Answer 2

Let the weight percentages of higher and lower price coffee beans in the blend be "a" % and "b" % respectively.   So, a+b=100 ··· Eq.1  And one pound of blended beans consists of (a/100) pounds of higher price beans, and (b/100) pounds of lower price beans.

Thus, the price of blended beans per pound can be written as shown below:

5.25(a/100)+3.25(b/100)=4.50   Multiply both sides by 100, getting

5.25a+3.25b=450   From Eq.1, we have: b=100-a   Plug this into the equation, getting

5.25a+3.25(100-a)=450   Solve the equation for a, we have:

a=62.5%   And from Eq.1, we also have: b=100-a=100-62.5=37.5%

Therefore, the total quantity of higher price beans is: 160x(a/100)=160x(62.5/100)=100 pounds,

and the total quantity of lower price beans is: 160-100=60 pounds.

The answer: She should blend 100 pounds of higher price beans with 60 pounds of lower price beans.