Proportion Problems Worksheet

1. A runner ran 4.9 miles yesterday and 7.7 miles today. What is the ratio of the distance she ran yesterday to the distance she ran today?
2. If a company has 10 management-level staff and 25 nonmanagement level staff, what is the ratio of managers to the entire staff of the company?
3. A house has a 9:2 ratio of windows to doors. If it has four doors, how many windows does it have?
4. A restaurant sells a 5 to 3 ratio of red wine to white wine. If it sells 14 more bottles of red wine than white wine in one night, how many bottles does it sell altogether?
5. Charles recently tracked his monthly spending and found that he spends 20% of his income on rent and 15% on transportation. If $3,250 goes to neither rent nor transportation, what is his rent each month? 6. A company has a 6 to 1 ratio of domestic to foreign sales revenue. It its total revenue last year was$350,000, how much of that was from foreign sales?
7. Jason can swim 9 laps in the time it takes his cousin Anton to swim 5 laps. If the two boys swam a combined total of 140 laps in the same time span, how many of those laps did Jason swim?
8. An organization has a 5:3:2 ratio of members from, respectively, Massachusetts, Vermont, and New Hampshire. If the organization has a total of 240 members, how many are from Vermont?
9. An organization has a 5:3:2 ratio of members from, respectively, Massachusetts, Vermont, and New Hampshire. If 42 of its members are from Vermont, how many members are from either of the other two states?
10. An organization has a 5:3:2 ratio of members from, respectively, Massachusetts, Vermont, and New Hampshire. If 60 members are from New Hampshire, how many are from Massachusetts?
11. A bookmobile has a 15 to 4 ratio of nonfiction books to fiction books. If it has 900 nonfiction books, how many books does it have altogether?
12. A diner has an 8:5 ratio of dinner customers to lunch customers. If it averages 40 lunch customers, what is its average number of customers for both lunch and dinner?

Solving Proportions

Have you ever played dominoes? In the standard set of dominoes,
7 out of 28 tiles, or one-fourth of the tiles, are doubles.

The ratios $$\frac{7}{28}$$ and $$\frac{1}{4}$$ are equivalent.
That is $$\frac{7}{28}$$ = $$\frac{1}{4}$$.
The equation $$\frac{7}{28}$$ = $$\frac{1}{4}$$ is an example of a proportion.

Percent of a Number

According to the graph, 20% of parents buy shoes for their children every four to five months. If 2,500 parents were surveyed, how many said that they purchase shoes for their children every four to five months? Continue reading Percent of a Number

Percents and Fractions

You’ll learn to express percents as fractions and vice versa. Knowing how to express a number in a different form can help you interpret a monthly budget.

You know that a 10 x 10 grid can be used to represent hundredths. Since the word percent means out of one hundred, you can also use a 10 x 10 grid to model percents.

Shade two fifths of the 10 x 10 grid. What percent have you modeled? Continue reading Percents and Fractions

Investigating Exponential Functions

Collect the Data
Step 1 Cut a sheet of notebook paper in half.
Step 2 Stack the two halves, one on top of the other.
Step 3 Make a table like the one below and record
the number of sheets of paper you have in the stack after one cut.
Step 4 Cut the two stacked sheets in half, placing the resulting pieces in a single stack. Record the number of sheets of paper in the new stack after 2 cuts.
Step 5 Continue cutting the stack in half, each time putting the resulting piles in a single stack and recording the number of sheets in the stack. Stop when the resulting stack is too thick to cut. Continue reading Investigating Exponential Functions

Measures of Variability

In this lesson we learn the concept of  variability  and how to compute three measures of the variability of a data set.

Data set 1: 10,8,12,10,9,13,10,9,10

Data set 2: 16,7,10,3,12,6,10,17,4,15

The mean, median and mode of both data sets is the same: 10

The range is the difference between the largest and the smallest value in the data set.

For Data set 1 the range is 13-8=5 and for the second is 17-3=14

The range indicates the size of the smallest interval which contains all the data.  Less variability means a smaller range.

Since the range is based solely on the two most extreme values within the data set, if one of these is either exceptionally high or low (outlier) it will result in a range that is not typical of the variability within that data set.

The sample variance for data set 1 is 2.1 and for the second data set is 22.4

The sample standard deviation is 1.5 for the first data set and 5 for the second data set