Question

(9 POINT QUESTION)A claw arcade machine contains stuffed animals and mystery boxes. There are 51 items in the machine. Winning a stuffed animal has twice as many favorable outcomes as winning a mystery box. How many of each item is in the machine?

Answer 1

51=2x+x
51=3x
/3 /3
17=x
Stuffed animal=2x
2x=34

Mystery box=x
x=17

Answer 2

There are 56 stuffed animals and 28 mystery boxes in the claw arcade machine

Firstly, we assign variables.

Let the number of stuffed animals be x and the number of mystery boxes be y

The probability of selecting a stuffed animal is x/84 while the probability is selecting a mystery box is y/84

Now, since the total probability can be 1:

This means that

x/84 + y/84 = 1 •••••••(i)

Now from the question, we were told that the probability of selecting or winning a stuffed animal is twice that of winning a mystery box

Thus x/84 = 2 * y/84

X/84 = y/42

Let’s substitute this into equation 1

y/42 + y/84 = 1

(2y+ y)/84 = 1

3y/84 = 1

3y = 84

y = 84/3

y = 28

Since x + y = 84

x = 84 - y

x = 84-28 = 56

Hope this helps!!