SOLUTION: How many pounds of Batangas coffee selling at Php47.50 per pound must be mixed to a foreign brand selling at Php32.50 per pound to produce a 30-pound mixture that will be sell for

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Question 1180955: How many pounds of Batangas coffee selling at Php47.50 per pound must be mixed to a foreign brand selling at Php32.50 per pound to produce a 30-pound mixture that will be sell for Php37.50?
Answer by greenestamps(13203) About Me  (Show Source):
You can put this solution on YOUR website!


(1) A usual typical algebraic setup....

x pounds at Php 32.50 per pound, plus (30-x) pounds at Php 47.50 per pound, equals 30 pounds at Php 37.50 per pound:

32.50%28x%29%2B47.50%2830-x%29=37.50%2830%29

Solve using basic algebra; I leave that to you.

(2) A quick and easy informal way to solve any mixture problem like this, if a formal algebraic solution is not required....

Consider the three prices on a number line: 32.50, 37.50, and 47.50.

Observe (or calculate) that 37.50 is 1/3 of the way from 32.50 to 47.50. (32.50 to 47.50 is a difference of 15; 32.50 to 37.50 is a difference of 5; 5/15 = 1/3).

That means 1/3 of the mixture is the more expensive coffee.

ANSWER: 1/3 of 30 pounds, or 10 pounds, of the Batangas coffee; the other 20 pounds of the foreign brand.

CHECK:
10(47.50)+20(32.50)= 475+650=1125
30(37.50)=1125