algebra mixture problem ?

Question

can you please help me?
i dont understand how to do this.
its so confusing =/
so yea please walk me through it step by step.

here is the problem :

A jar of M&M's that has 40% blue M&M's is mixed with a jar of M&M's that has 60% blue M&M's to obtain 200 grams of a jar with 50% blue M&M's/ How many grams of the 40% blue M&M's should be added?

thank you

Answer 1

Using algebra, let
x= the number of grams of the 40% blue M&Ms added (x is what you are looking for),
then 200-x would have to be the number of grams for the 60% blues.
The equation becomes: 40%(x) + 60%(200-x) = 50%200
Take it from there:
0.4x +120 - 0.6x = 100
-0.2 x = -20
x = 100
add 100 grams of the 40% blues.
(You can get this through logic, but you are learning to use algebra.)

Answer 2

OK. lets do this with a logic approach

Jar A = 40%
Jar B = 60%

If you pull 10 m's from Jar A.. four of them will be blue
if you pull 10 m's from Jar B 6 of them will be blue

if you put those 20 into a new jar 10 of them or 50% will be blue

so..if you take 100 grams from each of the jars (assuming that blue and non-blue m's weigh the same (and are identical in size/mass) you will end up with 200 grams of a 50/50 mixture.

.

Answer 3

Since 40% and 60% average to 50%, you need half of the container to come from the 40% jar.

So 100grams of the 40% blue M&Ms