# Math question?

Sarah Meeham blends coffee for​ Tasti-Delight. She needs to prepare 170 pounds of blended coffee beans selling for ​\$3.56 per pound. She plans to do this by blending together a​ high-quality bean costing ​\$4.75 per pound and a cheaper bean at ​\$2.50 per pound. To the nearest​ pound, find how much​ high-quality coffee bean and how much cheaper coffee bean she should blend.

Relevance
• 4.75 * x + 2.5 * y = 3.56 * (x + y)

4.75 * x + 2.5 * y = 3.56 * x + 3.56 * y

1.19 * x = 1.06 * y

119x = 106y

x + y = 170

x = 170 - y

119 * (170 - y) = 106 * y

119 * 170 - 119 * y = 106 * y

119 * 170 = 225 * y

119 * 34 * 5 = 45 * 5 * y

119 * 34 = 45 * y

7 * 17 * 2 * 17 = 45 * y

14 * 17^2 = 45 * y

14 * 289 / 45 = y

28 * 289 / 90 = y

28 * 28.9 / 9 = y

(27 + 1) * (28.8 + 0.1) / 9 = y

y = 27 * 28.8 / 9  +  27 * 0.1 / 9  +  28.8 * 1 / 9  +  1 * 0.1 / 9

y = 3 * 28.8 + 0.3 + 3.2 + 0.0111111.....

y = 86.4 + 3.5 + 0.011111.....

y = 89.9 + 0.0111111....

y = 89.91111111......

x = 170 - 89.911111.....

x = 80.0888888888.......

90 lbs of the cheaper coffee and 80 lbs of the more expensive coffee

• Anonymous
9 months ago

Let X be the lbs of the HQ beans

170 lbs * \$3.65 = X * \$4.75 + (170 lbs - X) * \$2.50