| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.67 |
| Score | 0% | 53% |
A sports card collection contains football, baseball, and basketball cards. If the ratio of football to baseball cards is 5 to 2 and the ratio of baseball to basketball cards is 5 to 1, what is the ratio of football to basketball cards?
| 25:2 | |
| 1:8 | |
| 1:2 | |
| 9:1 |
The ratio of football cards to baseball cards is 5:2 and the ratio of baseball cards to basketball cards is 5:1. To solve this problem, we need the baseball card side of each ratio to be equal so we need to rewrite the ratios in terms of a common number of baseball cards. (Think of this like finding the common denominator when adding fractions.) The ratio of football to baseball cards can also be written as 25:10 and the ratio of baseball cards to basketball cards as 10:2. So, the ratio of football cards to basketball cards is football:baseball, baseball:basketball or 25:10, 10:2 which reduces to 25:2.
If the ratio of home fans to visiting fans in a crowd is 3:1 and all 50,000 seats in a stadium are filled, how many home fans are in attendance?
| 30,400 | |
| 37,500 | |
| 24,000 | |
| 28,800 |
A ratio of 3:1 means that there are 3 home fans for every one visiting fan. So, of every 4 fans, 3 are home fans and \( \frac{3}{4} \) of every fan in the stadium is a home fan:
50,000 fans x \( \frac{3}{4} \) = \( \frac{150000}{4} \) = 37,500 fans.
A machine in a factory has an error rate of 4 parts per 100. The machine normally runs 24 hours a day and produces 9 parts per hour. Yesterday the machine was shut down for 4 hours for maintenance.
How many error-free parts did the machine produce yesterday?
| 97.7 | |
| 114.7 | |
| 172.8 | |
| 102.3 |
The hourly error rate for this machine is the error rate in parts per 100 multiplied by the number of parts produced per hour:
\( \frac{4}{100} \) x 9 = \( \frac{4 \times 9}{100} \) = \( \frac{36}{100} \) = 0.36 errors per hour
So, in an average hour, the machine will produce 9 - 0.36 = 8.64 error free parts.
The machine ran for 24 - 4 = 20 hours yesterday so you would expect that 20 x 8.64 = 172.8 error free parts were produced yesterday.
Solve 3 + (3 + 5) ÷ 5 x 5 - 32
| 2 | |
| 1\(\frac{1}{8}\) | |
| 2\(\frac{1}{3}\) | |
| \(\frac{4}{7}\) |
Use PEMDAS (Parentheses, Exponents, Multipy/Divide, Add/Subtract):
3 + (3 + 5) ÷ 5 x 5 - 32
P: 3 + (8) ÷ 5 x 5 - 32
E: 3 + 8 ÷ 5 x 5 - 9
MD: 3 + \( \frac{8}{5} \) x 5 - 9
MD: 3 + \( \frac{40}{5} \) - 9
AS: \( \frac{15}{5} \) + \( \frac{40}{5} \) - 9
AS: \( \frac{55}{5} \) - 9
AS: \( \frac{55 - 45}{5} \)
\( \frac{10}{5} \)
2
In a class of 26 students, 7 are taking German and 13 are taking Spanish. Of the students studying German or Spanish, 2 are taking both courses. How many students are not enrolled in either course?
| 20 | |
| 21 | |
| 18 | |
| 8 |
The number of students taking German or Spanish is 7 + 13 = 20. Of that group of 20, 2 are taking both languages so they've been counted twice (once in the German group and once in the Spanish group). Subtracting them out leaves 20 - 2 = 18 who are taking at least one language. 26 - 18 = 8 students who are not taking either language.