imagodsobeit

Original question:

A lemonade recipe calls for using a ratio of 2 cups of lemon juice for every 4 cups of water. What is the ratio of lemon juice to water?

This problem asks for the ratio of lemon juice to water. We are given both values, so it's just a proportion. 

2 (cups of lemon juice) : 4 (cups of water)

which simplifies down to 1:2

If it's just 0.3, it's 3/10, as the 3 is simply moved after the decimal point once.

However, if youre talking about 0.3333... (3 repeats forever), then it's 1/3, and we can use math to prove it. Each time you divide 3 into 1, it's impossible, so you always borrow a 0 from the next decimal place. That always returns 1, and we can see that it becomes recursive. Therefore, we are left with a repeating decimal, which is represented in a fraction as 1/3.

Guess and check.

If every batch is fudge: 9x3=27

If every batch is peanut butter: 9x10=90

Each time we replace a peanut butter batch with a fudge batch, 7 brownies are deducted from the total. 

90-62=28 difference between all PB and actual amount

28/7=4 batches of fudge

9-4=5 batches of PB

There are 4 batches of fudge and 5 batches of PB.

(doing backwards to prove it's correct)

4x3=12 

5x10=50

12+50=62

For this problem, you can guess and check.

If we have 7 bags of 9 apples, it totals 63 apples.

If we have 7 bags of 5 apples, it toals 35 apples.

Each time we replace a bag of 9 apples with 5, it deducts 4 apples from the total.

63-51=12 apple difference from 7 bags of 9 apples from the actual number of apples

12/4=3 bags of red apples

7-3=4 bags of green apples

Therefore, there are 4 bags of green apples and 3 bags of red apples.

(doing it backwards to prove that it's correct)

4x9=36

3x5=15

36+15=51.