The ratio of Melanie’s allowance to Jacob’s allowance is 4.1 to 20.5. If Jacob gets $5.00, how much allowance does Melanie get?
The Correct Answer and Explanation is:
To solve the problem, we first interpret the ratio and then calculate Melanie’s allowance based on Jacob’s.
Step-by-step Solution:
We’re given:
- The ratio of Melanie’s allowance to Jacob’s allowance is 4.1 to 20.5.
- Jacob receives $5.00.
- We need to find out how much Melanie receives.
Step 1: Simplify the Ratio
We simplify the ratio 4.1:20.5 by dividing both parts by the same number — the greatest common divisor. In this case, we can divide both numbers by 4.1:4.14.1:20.54.1=1:5\frac{4.1}{4.1} : \frac{20.5}{4.1} = 1 : 54.14.1:4.120.5=1:5
So the simplified ratio is 1:5. This means for every $1 Melanie receives, Jacob receives $5.
Step 2: Use the Simplified Ratio
Now that we know the ratio is 1:5 and Jacob receives $5.00, we can use proportion to find Melanie’s allowance.
Let MMM represent Melanie’s allowance. Then:M5.00=15\frac{M}{5.00} = \frac{1}{5}5.00M=51
Now solve for MMM:M=15×5.00=1.00M = \frac{1}{5} \times 5.00 = 1.00M=51×5.00=1.00
✅ Final Answer:
Melanie receives $1.00.
Explanation
Ratios are used to compare two quantities. In this case, the ratio 4.1:20.5 tells us the relationship between Melanie’s and Jacob’s allowances. However, ratios can often be simplified to make calculations easier. To simplify a ratio, we divide both parts by the same non-zero number. Here, dividing both 4.1 and 20.5 by 4.1 gives a simpler 1:5 ratio.
This simplified ratio shows that for every 1 part Melanie receives, Jacob receives 5 parts. So, if Jacob gets $5.00, each “part” of the ratio must be worth $1.00 (since 5 parts × $1.00 = $5.00). Therefore, Melanie receives 1 part, or $1.00.
This approach helps when dealing with any proportional situation, including budgeting, recipes, or any scenario where two amounts are related by a fixed ratio. Simplifying the ratio first makes the math straightforward, helping avoid errors when setting up proportions. Always remember: once a ratio is simplified, it’s easy to apply it to real-world values using basic multiplication or cross-multiplication
.