Solving Proportions
Directions: Solve the following proportions.
1. Rafi took a total of 16 pages of notes during 4 hours of class. After attending 5 hours of class, how many total pages of notes will Rafi have in his notebook?
2. Edward spent 6 minutes on the phone while routing 3 phone calls. In all, how many phone calls does Edward have to route to spend a total of 10 minutes on the phone?
3. Josiah jarred 6 liters of jam after 2 days. How many days does Josiah need to spend making jam if he wants to jar 12 liters of jam in all?
4. Evan's office recycled a total of 8 kilograms of paper over 2 weeks. How many weeks will it take Evan's office to recycle a total of 20 kilograms of paper?
5. Emma baked 15 cookies with 3 scoops of flour. With 4 scoops of flour, how many cookies can Emma bake?
1. In all 20
2. In all 5
3. In all 4
4. In all 5
5. In all 20
These are all proportions, done in the same way.
In each case, set your ratio equal to the one which is constant.
#1. x/5 = 16/4
To solve these proportions, we will use the concept of ratios. A proportion is a statement that two ratios are equal.
To solve a proportion, we will set up a ratio with the given information and find the missing value by cross-multiplying and then solving for the unknown variable.
Let's solve each proportion step by step:
1. Rafi took a total of 16 pages of notes during 4 hours of class. After attending 5 hours of class, how many total pages of notes will Rafi have in his notebook?
Let's set up the ratio:
Pages of notes / Hours of class = Pages of notes / Hours of class
Let's substitute the given values:
16 / 4 = x / 5
Cross-multiply:
16 * 5 = 4 * x
80 = 4x
Now, solve for x:
x = 80 / 4
x = 20
Therefore, after attending 5 hours of class, Rafi will have a total of 20 pages of notes in his notebook.
2. Edward spent 6 minutes on the phone while routing 3 phone calls. In all, how many phone calls does Edward have to route to spend a total of 10 minutes on the phone?
Let's set up the ratio:
Minutes on the phone / Number of phone calls = Minutes on the phone / Number of phone calls
Let's substitute the given values:
6 / 3 = x / 10
Cross-multiply:
6 * 10 = 3 * x
60 = 3x
Now, solve for x:
x = 60 / 3
x = 20
Therefore, Edward needs to route a total of 20 phone calls to spend a total of 10 minutes on the phone.
3. Josiah jarred 6 liters of jam after 2 days. How many days does Josiah need to spend making jam if he wants to jar 12 liters of jam in all?
Let's set up the ratio:
Liters of jam / Number of days = Liters of jam / Number of days
Let's substitute the given values:
6 / 2 = 12 / x
Cross-multiply:
6 * x = 12 * 2
6x = 24
Now, solve for x:
x = 24 / 6
x = 4
Therefore, Josiah needs to spend 4 days making jam to jar a total of 12 liters.
4. Evan's office recycled a total of 8 kilograms of paper over 2 weeks. How many weeks will it take Evan's office to recycle a total of 20 kilograms of paper?
Let's set up the ratio:
Kilograms of paper / Number of weeks = Kilograms of paper / Number of weeks
Let's substitute the given values:
8 / 2 = 20 / x
Cross-multiply:
8 * x = 20 * 2
8x = 40
Now, solve for x:
x = 40 / 8
x = 5
Therefore, it will take Evan's office 5 weeks to recycle a total of 20 kilograms of paper.
5. Emma baked 15 cookies with 3 scoops of flour. With 4 scoops of flour, how many cookies can Emma bake?
Let's set up the ratio:
Number of cookies / Number of scoops of flour = Number of cookies / Number of scoops of flour
Let's substitute the given values:
15 / 3 = x / 4
Cross-multiply:
15 * 4 = 3 * x
60 = 3x
Now, solve for x:
x = 60 / 3
x = 20
Therefore, with 4 scoops of flour, Emma can bake a total of 20 cookies.
I hope this helps! Let me know if you have any other questions.