Percentage question

Question

So I was working on this SAT question and I got stuck on one question:

"If 1 cup of milk is added to a 3-cup mixture that is 2/5 flour and 3/5 milk, what percent of the 4-cup mixture is milk?"

I looked through every explanation but they didn't really help. Could you explain it step by step?

Answer 1

Very simple and straightforward.

We are just interested in the % of milk. Thus,

Total milk % = (3/5 of 3 cups + 1 cup) out of 4 cups = ( 3/5 * 3 + 1 ) / 4 = 2.8 / 4 = 0.7 = 70%

Answer 2

START:

"3-cup mixture that is 2/5 flour and 3/5 milk"

ADD:

"1 cup of milk is added"

-----------------

4-cups with (2/5)3 flour and (3/5)3 + 1 milk

TOTAL volume is 4 cups (assuming that flower retains its previous volume amount and does not dissolve differently).

.

Milk = 9/5 + 5/5 = 14/5 cups

Percent of milk = 100% * (14/5) / 4 [to divide by 4/1. multiply by 1/4 ]

= 100% * ( 14/5 ) * (1/4)

= 100% * 14/20

= 100% * 70/100

= 70%

Note: We started with 60% milk, so adding milk should raise the percentage of milk.

Answer 3

3 cups = 2/5 flour + 3/5 milk + 2 cups of something else

the final mixture contains 4 cups, 1 and 3/5 of which is milk.

(1 and 3/5) divided by 4 =

(8/5) divided by 4/1 =

8/5 * 1/4 = 8/20 = 2/5 = 0.4 = 40%