A picnic cooler contains different types of cola.12 regular, 8 cherry, 6 diet, 8 caffeine free, 10 diet vanilla, and some diet cherry. U pick a can of cola without looking at its type. There is a 44% chance that the drink selected is diet. How many diet cherry colas r in the cooler? Hint: let c.rep the diet cherry cola, remember that 44% can be written as a fraction. (10 marks)

Question

A picnic cooler contains different types of cola.12 regular, 8 cherry, 6 diet, 8 caffeine free, 10 diet vanilla, and some diet cherry. U pick a can of cola without looking at its type. There is a 44% chance that the drink selected is diet. How many diet cherry colas r in the cooler? Hint: let c.rep the diet cherry cola, remember that 44% can be written as a fraction. (10 marks)

Answer 1

I got 6 as the answr when I did the check it worked! Thanks for the help tho! :)

Answer 2

Let's solve this problem step-by-step:

Step 1: Set up the equation
The total number of colas in the cooler is 12 (regular) + 8 (cherry) + 6 (diet) + 8 (caffeine-free) + 10 (diet vanilla) + c (diet cherry). This can be represented as:
12 + 8 + 6 + 8 + 10 + c = total number of colas

Step 2: Calculate the fraction
The problem states that there is a 44% chance of selecting a diet cola. We can write this as a fraction: 44/100 = 11/25.

Step 3: Set up the equation for the fraction
To calculate the fraction of diet colas in the cooler, we divide the number of diet colas (6 + c) by the total number of colas.
(6 + c) / (12 + 8 + 6 + 8 + 10 + c) = 11/25

Step 4: Solve the equation
To solve the equation, we cross multiply:
25 * (6 + c) = 11 * (12 + 8 + 6 + 8 + 10 + c)
150 + 25c = 55 + 27c

Step 5: Simplify the equation
Rearranging the equation, we get:
25c - 27c = 55 - 150
-2c = -95

Step 6: Solve for c
Divide by -2 on both sides:
c = -95 / -2
c = 47.5

Step 7: Interpret the result
Since the number of colas must be a whole number, we cannot have 47.5 diet cherry colas in the cooler. Therefore, there must be no diet cherry colas in the cooler.

Answer 3

To solve this problem, we need to use the hint provided in the question. Let's start by setting up the equation.

Let c represent the number of diet cherry colas in the cooler.

We know that the total number of colas in the cooler is given as:
Regular colas + Cherry colas + Diet colas + Caffeine-free colas + Diet Vanilla colas + Diet Cherry colas

Therefore, the total number of colas can be expressed as:
12 + 8 + 6 + 8 + 10 + c

Now, we need to determine the probability of selecting a diet cola, which is given as 44%. This can be expressed as a fraction as well, where the numerator is the number of diet colas and the denominator is the total number of colas:
Number of diet colas / Total number of colas = 44% = 44 / 100

Using the value we derived for the total number of colas:
(6 + 10 + c) / (12 + 8 + 6 + 8 + 10 + c) = 44 / 100

Simplifying this equation, we have:
(16 + c) / (44 + c) = 44 / 100

Now, let's solve this equation:
100(16 + c) = 44(44 + c)
1600 + 100c = 1936 + 44c
100c - 44c = 1936 - 1600
56c = 336
c = 6

Therefore, there are 6 diet cherry colas in the cooler.

Answer 4

let c be the number of diet cherry drinks

total drinks = 12+8+6+8+10+c = 52+c
diet drinks = 6+10 + c
= 16+c , I didn't count caffeine free as diet

(16+c)/(52+c) = 44/100 = 11/25
400 + 25c = 572 + 11c
14c = 172
c = a fraction, ---> should not be a fraction, should be a whole number

let's count caffeine free as diet
number of diet = 24+c

(24+c)/(52+c) = 11/25
600+25c = 572 + 11c
14c = a negative, this is even worse !!!

Unless I misread the question, the question is bogus.