Question
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A survey of Year 8 students shows that of students walk to school, one-sixth ride their bike and
the remainder catch the bus.
2 What is the ratio of students who walk to those who ride to those who catch the bus, among this
year level?
A
B
C
D

Ask by Ball Todd. in Australia
Dec 09,2024

Upstudy AI Solution

Tutor-Verified Answer

Answer

The ratio of students who walk to those who ride to those who catch the bus is 12:5:13.

Solution

To find the ratio of students who walk, ride their bike, and catch the bus, we start by determining the proportions of each group based on the information given.
  1. Walking to school:
    • of students walk to school. This can be expressed as a fraction:
  2. Riding a bike:
    • One-sixth of the students ride their bike. This can be expressed as a fraction:
  3. Catching the bus:
    • The remainder of the students catch the bus. To find this, we first calculate the total percentage of students who walk and ride their bike:
    • Therefore, the percentage of students who catch the bus is:
Now we have the proportions:
  • Walking:
  • Riding:
  • Catching the bus:
Next, we convert these proportions into a ratio. To do this, we can express each proportion as a fraction of a common denominator. The least common multiple of the denominators (1, 6, and 1) is 6.
  • Walking:
  • Riding:
  • Catching the bus:
Now we can express the ratios:
  • Walking:
  • Riding:
  • Catching the bus:
Thus, the ratio of students who walk to those who ride to those who catch the bus is:
To simplify this ratio, we can divide each term by 2:
Thus, the final ratio of students who walk to those who ride to those who catch the bus is:
The correct answer is C .

Answered by UpStudy AI and reviewed by a Professional Tutor

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Explain
Simplify this solution

Mind Expander

To determine the ratio of students who walk, ride their bike, and catch the bus, let’s first analyze the proportions based on the survey data.
  1. Percentage of Students Walking: 40% walk to school.
  2. Percentage of Students Riding Bikes: One-sixth of the students ride their bikes, which is approximately 16.67%.
  3. Percentage of Students Catching the Bus: To find this, we need to calculate the remainder. The total percentage is 100%, so:
    • Percentage catching the bus = 100% - 40% (walking) - 16.67% (riding) = 43.33%.
Now, we can convert these percentages into a common format for the ratio:
  • Walking: 40% = 40 parts
  • Riding: 16.67% ≈ 16.67 parts
  • Catching the bus: 43.33% ≈ 43.33 parts
To express them all in a simplified whole number format, we can convert the percentages to equivalent fractions for easier comparison, or just round consistently. A simplified common multiple logic would yield:
  • Walking: 40 → 120
  • Riding: 16.67 → 50
  • Catching the bus: 43.33 → 130
Thus, the ratio will simplify approximately to:
Walking : Riding : Catching = 120 : 50 : 130
By further simplifying this we divide by 10 which gives us:
12 : 5 : 13
So, the correct answer is C .

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