- Which of the following are the lowest terms for expressing the ratio of the percentage of juniors majoring in Spanish to the percentage of juniors majoring in history?
- 14:36
- 14:22
- 7:11
- 7:18
- 14:18
The percentage of juniors majoring in Spanish is 14. The percentage of juniors majoring in history is 36. The ratio 14:36 in lowest terms is 7:18.
- If a restaurant’s salad dressing is made entirely of oil and vinegar at a ratio of \(\frac{3}{4}\) cup oil to \(\frac{1}{4}\) cup vinegar, how many cups of vinegar are there in six cups of salad dressing?
- \(\frac{1}{2}\)
- 1\(\frac{1}{2}\)
- 1\(\frac{3}{4}\)
- 2\(\frac{1}{2}\)
Vinegar is \(\frac{1}{4}\) cup and the salad dressing as a whole is \(\frac{1}{4}\) cup of vinegar plus \(\frac{3}{4}\) cup oil, which equals 1 cup total. Thus, vinegar is \(\frac{1}{4}\) of the salad dressing. Therefore, \(\frac{1}{4}\) of six cups is \(\frac{3}{2}\) or 1\(\frac{1}{2}\) cups of vinegar.
- A classroom has 15 boys and 13 girls. If 10 more girls join the class, what is the ratio of girls to boys?
- 15:23
- 13:15
- 10:15
- 23:15
First, calculate how many girls there will be after 10 more join the class:
\(13 + 10 = 23\)
Then, express the number of girls compared to boys as the ratio 23:15.
- The ratio of left-handed to right-handed ballplayers on the girls’ softball team is 2:3. If there are 12 left-handed players on the team, how many girls are on the roster in all?
- 18
- 24
- 30
- 32
The ratio of left- to right-handed players will be proportional to the ratio 2:3. Therefore, \(\frac{2}{3}=\frac{12}{R}\), so that by cross-multiplying we get \(2R = 36\) or \(R = 18\) right-handed players. The total number on the roster is therefore \(12 + 18 = 30\).
- The ratio of blue food coloring to yellow food coloring used in making green cake frosting is 3 to 2. If 18 drops of blue food coloring are used, how many drops of yellow food coloring are needed?
- 2
- 6
- 8
- 12
Set up and solve a proportion, as shown below, where is the number of drops of yellow food coloring. To solve the proportion, cross-multiply:
\(\frac{3}{2}=\frac{18}{x}\)
\(3x = 36\)
\(x = 12\)
- Hunter planted a combination of tomatoes, broccoli, and bell peppers in a ratio of 3:2:1 in his garden. If the garden had a total of 72 plants, how many tomatoes are in his garden?
- 12
- 24
- 32
- 36
A ratio of 3:2:1 gives a whole of 6 (in other words, in each set of six plants, there are three tomato plants, two broccoli plants, and one bell pepper plant). It takes 12 sets of six plants to total 72 plants. To determine how many tomatoes Hunter planted, multiply \(3 \times 12\) for a total of 36.
- Which of the following expressions represents the ratio of the circumference of a circle to its area?
- \(1:\pi r^2\)
- \(1:\frac{\pi r^2}{2\pi}\)
- \(1:\frac{2\pi r}{r^2}\)
- \(1:2\pi r^{\frac{1}{2}}\)
- \(1:\frac{r}{2}\)
The area of the circle is \(\pi r^2\), while the circumference is \(2\pi r\). Taking the ratio of these two expressions and reducing gives the following:
\(2\pi r:\pi r^2=1:\frac{r}{2}\)
- In the figure below, A, B, and C are points on the number line, where O is the origin. What is the ratio of the distance \(BC\) to distance \(AB\)?
- 3:5
- 8:5
- 8:11
- 3:11
- 8:6
Since the figure represents the number line, the distance from point A to point B will be the difference \(B – A\), which is \(5 – (-6) = 11\). Likewise, the distance from point B to point C will be the difference \(C – B\), which is \(8 – 5 = 3\). So the ratio of the distances \(BC\) to \(AB\) will be 3:11.
- Approximately 40,000 obstetricians are registered in the US. There are an estimated 440,000 midwives in the country. What is the ratio of midwives to obstetricians?
- 8:1
- 12:1
- 11:1
- 7:1
To find the ratio, divide the number of midwives by the number of obstetricians. This yields \(440,000 \div 40,000 = 11\). Therefore, the ratio is 11:1.
- Approximately 40,000 obstetricians are registered in the US. There are an estimated 440,000 midwives in the country. What is the ratio of midwives to obstetricians?
- 1
- 9
- 12
- 20
You are given the total number of students in the class and the fraction of students who are boys. With this information, you can determine the number of boys by multiplying \(\frac{2}{3}\) by 27. You will find that there are 18 boys in the class. You can then find the number of girls by subtracting the number of boys from the total number of students:
\(27 – 18 = 9\)
- A solution contains 6% calcium. How many milliliters of solution can be made from 50 ml of calcium?
- 833
- 952
- 1,054
- 2,000
Set up a ratio of \(\frac{6}{100}=\frac{50}{x}\) , with \(x\) equal to the total number of milliliters of solution. Then, solve by cross multiplying:
\(6x = 5,000\)
\(x = \frac{5,000}{6} = 833\)