Three friends all pitch in to buy some pizza. Annie, Billy, and Chuck each gave money in the ratio of 3:5:4 respectively. If the total amount collected was $15, how much money did Billy put in? dollars.
The Correct Answer and Explanation is :
Let’s solve this problem step-by-step:
Step 1: Understand the ratio
The ratio of money contributed by Annie, Billy, and Chuck is given as 3:5:4. This means that for every 3 parts Annie contributed, Billy contributed 5 parts, and Chuck contributed 4 parts.
Step 2: Find the total number of parts
To calculate how much money each person contributed, first determine the total number of parts. Add the parts of the ratio:
[
3 + 5 + 4 = 12 \text{ parts}
]
This tells us that the total contribution is divided into 12 equal parts.
Step 3: Determine the value of one part
The total money collected is $15. To find out the value of one part, divide the total amount by the total number of parts:
[
\frac{15}{12} = 1.25 \text{ dollars per part}
]
Step 4: Calculate Billy’s contribution
Billy contributed 5 parts, so to find how much Billy put in, multiply the value of one part by 5:
[
5 \times 1.25 = 6.25 \text{ dollars}
]
Thus, Billy put in $6.25.
Explanation
The key to solving this problem is understanding how the ratio works. When three people contribute in a given ratio (3:5:4), it means their individual contributions are proportional to these numbers. By dividing the total money into 12 parts, we can then calculate how much each part is worth. Multiplying the number of parts that Billy contributed (5 parts) by the value of one part (1.25 dollars) gives us Billy’s total contribution.
This method allows us to fairly distribute the $15 according to the given ratio, ensuring that each person’s contribution reflects the proportions set by the problem.