SOLUTION: abby mixes cinnamon and nutmeg to make 25g of spice mix. Cinnamon costs 9 cents/g and nutmeg costs 12.5 cents/g. The spice mix costs 9.7 cents/g. How much of each spice does abby n

Algebra ->  Equations -> SOLUTION: abby mixes cinnamon and nutmeg to make 25g of spice mix. Cinnamon costs 9 cents/g and nutmeg costs 12.5 cents/g. The spice mix costs 9.7 cents/g. How much of each spice does abby n      Log On


   

Question 1187869: abby mixes cinnamon and nutmeg to make 25g of spice mix. Cinnamon costs 9 cents/g and nutmeg costs 12.5 cents/g. The spice mix costs 9.7 cents/g. How much of each spice does abby need to use?
Found 2 solutions by josgarithmetic, greenestamps:
Answer by josgarithmetic(39616) About Me  (Show Source):
You can put this solution on YOUR website!
                   PRICE        QUANTITY     COST     
CINNAMON             9            25-n       9(25-n)
NUTMEG              12.5           n         12.5n
FINISH               9.7          25         9(25-n)+12.5n

9.7%2A25=9%2825-n%29%2B12.5n-----------

Answer by greenestamps(13198) About Me  (Show Source):
You can put this solution on YOUR website!


Here is a quick informal way to solve any "mixture" problem like this -- if a formal algebraic solution is not required.

Where the cost per gram of the mixture lies between the costs per gram of each ingredient determines the ratio in which the two ingredients must be mixed.

Look at the three costs per gram on a number line -- 9, 9.7, and 12.5 -- and observe/calculate that 9.7 is 1/5 of the way from 9 to 12.5: (9.7-9)/(12.5-9) = 0.7/3.5 = 1/5

That means 1/5 of the mixture is the more expensive ingredient.

ANSWER: 1/5 of 25g, or 5g, of nutmeg; the other 20g of cinnamon