Write each proportion as described. Be sure to simplify your answer. If there ar

Question

Write each proportion as described. Be sure to simplify your answer. If there are 26 students in a class and 12 are seniors, what proportion of students are not seniors? Out of 1000 people surveyed, 850 said they liked soda. What proportion of the people surveyed said they do not like soda? Answer each question. Round your answer to the nearest hundredth when necessary. If six out of every ten individuals in a population carry a gene for a defective enzyme, how many individuals carry the normal gene in a population of 990? The ratio of apples to oranges in a basket is 3 to 4. What fraction of fruit in the basket consists of apples? A 180-pound student burns 120 calories every half hour playing ultimate Frisbee. How many calories would he burn in a. 10 minutes? b. One hour and 45 minutes?

Explanation / Answer

1. Given

The total number of students (T) = 26

Total number of students who are senior (X) = 14

Solution

Total number of students who are not senior (Y) = 26-14 = 12

Proportion of students who are not senior = Y/T = 12/26 = 6/13 = 0.4615

Answer

  6/13

2. Going by the similar approach as stated in Answer 1, the only difference is the values of X, Y and T

Given

T = 1000 <= Total number of students in the class

X = 850 <= Students who like soda

Solution

Those who dont like soda (Y) = T - X = 1000 - 850 = 150

Proportion = (T - X) / T = 150/1000 = 3/20 = 0.15

Answer

3/20 = 0.15

3. The approach here would be similar to that for question 1 and 2, except that now we have to calculate the actual/absolute value based on that proportion.

Given

Total population (T) = 990

Proportion of people who carry the defective gene enzyme (X) = 6/10 = 3/5

Solution

The proportion of people who would not carry the defective gene enzyme (Y) = 1 - 3/5 = 2/5

The value of 1 is very important here. Always remeber that the sum total of proportions should lead to unit. For example there are two proportions of 2/3 and 1/3, then the sum would be always 1. Similary here, if every 6 individual out of 10 individual is carrying the defective gene enzyme, that means the remaining 4 individual are defective gene enzyme free.

Number of people who would not carry the defective gene enzyme = Y * T = 2/5 * 990= 396

Answer

396 individuals are without the defecitve enzyme

4. Given

  The ratio of apples to oranges = 3/4

Solution

Now , we have to find the fraction of fruits which are apples. Before, we move ahead with the solution, let us understand the concept of ratios. We are given with a ratio of apples to oranges, but we dont know the actual quantity of apples or oranges. It can be any multiple of 3 such as 6,12 and any multiple of 4 such as 4,8 etc. This ambiguity should come into our solution, so we need to maintain the homogenity of the equation.

The simplification of the numerator and denominator would happen with a single common multiple between the two. This quanity is unknown, let us assume it is 'x'.

Therefore, Apples = 3x and Oranges = 4x

Total fruits = 7x

Ratio of Apples in the basket = Apples / Total fruits = 3/7

Answer

3/7

5. Given

  Weight of the student = 180 pounds

Calories burnt every half hour = 120

Solution

  This is a classic example of giving unwanted details to confuse in the final solution. The current weight of the student is unwanted here and the only requirement is calories burnt.

So,

Calories burnt every half hour or 30 minutes (X) = 120

which implies that

a. Calories burnt every 10 minutes = X/3 = 40 Calories

This answers our first part.

b. Calories burnt per minute = 120/30 = 4

which implies that

Calories burnt per hour = 60*4 = 240

Calories burnt in 45 minutes = 180

Total Calories burnt in 1 hour 45 minutes = 420 Calories

Answer

a. 10 Calories b. 420 Calories

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