Answer:
Example 1:
In a bag of red and green sweets, the ratio of red sweets to green sweets is 3:4. If the bag contains 120 green sweets, how many red sweets are there?
Solution:
Step 1: Assign variables :
Let x = red sweets
Write the items in the ratio as a fraction.
red/green
Step 2: Solve the equation
Cross Multiply
3 × 120 = 4 × x
360 = 4x
Isolate variable x
x=360/4
Answer: There are 90 red sweets.
Example 2:
John has 30 marbles, 18 of which are red and 12 of which are blue. Jane has 20 marbles, all of them either red or blue. If the ratio of the red marbles to the blue marbles is the same for both John and Jane, then John has how many more blue marbles than Jane?
Solution:
Step 1: Sentence: Jane has 20 marbles, all of them either red or blue.
Assign variables:
Let x = blue marbles for Jane
20 – x = red marbles for Jane
We get the ratio from John
John has 30 marbles, 18 of which are red and 12 of which are blue.
red/blue
We use the same ratio for Jane.
red/blue
Step 2: Solve the equation
Cross Multiply
3 × x = 2 × (20 – x)
3x = 40 – 2x
Isolate variable x
x=40/5
John has 12 blue marbles. So, he has 12 – 8 = 4 more blue marbles than Jane.
Answer: John has 4 more blue marbles than Jane.
Explanation: