Finn has some sweets in a bag.
5 of the sweets are lemon flavored.
7 of the sweets are strawberry flavored.
The rest of the sweets are mint flavored.
The probability that Finn takes a mint flavored sweet is [tex]$\frac{2}{5}$[/tex]
How many mint flavored sweets are in the bag?
Answer (1)
Find the total number of sweets: 5 + 7 + m = 12 + m .
Set up the probability equation: 12 + m m = 5 2 .
Solve for m : 5 m = 2 ( 12 + m ) ⇒ 3 m = 24 ⇒ m = 8 .
State the number of mint sweets: 8 .
Explanation
Analyze the problem Let's analyze the problem. We know there are 5 lemon sweets and 7 strawberry sweets. The number of mint sweets is unknown, let's call it 'm'. The probability of picking a mint sweet is 2/5. We need to find the value of 'm'.
Find the total number of sweets The total number of sweets in the bag is the sum of lemon, strawberry, and mint sweets, which is 5 + 7 + m = 12 + m .
Set up the probability equation The probability of picking a mint sweet is the number of mint sweets divided by the total number of sweets, which is 12 + m m . We are given that this probability is 5 2 . So, we have the equation: 12 + m m = 5 2
Solve for m To solve the equation 12 + m m = 5 2 , we can cross-multiply: 5 m = 2 ( 12 + m ) 5 m = 24 + 2 m Subtract 2 m from both sides: 3 m = 24 Divide both sides by 3: m = 3 24 m = 8
State the final answer Therefore, there are 8 mint flavored sweets in the bag.
Examples
Imagine you are at a candy store. There are different flavors of candies in a jar, and you want to know how many candies of a particular flavor are in the jar. If you know the probability of picking that flavor and the number of other flavors, you can calculate the number of that particular flavor. For example, if you know that the probability of picking a cherry candy is 2/5, and there are 5 lemon and 7 orange candies, you can calculate that there are 8 cherry candies in the jar.
