Genevieve is cutting a 60-inch piece of ribbon into a ratio of [tex]$2:3$[/tex]. Since 2 inches are frayed at one end of the ribbon, she will need to start 2 inches in. This is indicated as 2 on the number line.
Where will her cut be located? Round to the nearest tenth.
[tex]$x=\left(\frac{m}{m+n}\right)\left(x_2-x_1\right)+x_1$[/tex]
A. 25.2 in.
B. 29.4 in.
C. 35.1 in.
D. 40.7 in.
Answer (2)
Identify the values: m = 2 , n = 3 , x 1 = 2 , x 2 = 62 .
Substitute the values into the formula: x = ( 2 + 3 2 ) ( 62 − 2 ) + 2 .
Simplify the expression: x = ( 5 2 ) ( 60 ) + 2 = 24 + 2 = 26 .
Round to the nearest tenth: The cut will be located at 26.0 inches.
Explanation
Understanding the Problem We are given the formula x = ( m + n m ) ( x 2 − x 1 ) + x 1 to find the location of the cut on a ribbon. We are also given that the ribbon is cut in a ratio of 2:3, with a frayed end starting at 2 inches.
Identifying the Values We need to identify the values for m , n , x 1 , and x 2 . From the problem, we have:
m = 2
n = 3
x 1 = 2 (starting point)
x 2 = 2 + 60 = 62 (ending point)
Substituting the Values Now, we substitute these values into the formula: x = ( 2 + 3 2 ) ( 62 − 2 ) + 2
Simplifying the Expression Next, we simplify the expression:
x = ( 5 2 ) ( 60 ) + 2
x = 5 2 × 60 + 2
x = 5 120 + 2
x = 24 + 2
x = 26
Finding the Cut Location The location of the cut is 26 inches. Since we need to round to the nearest tenth, we can write it as 26.0 inches.
Final Answer Therefore, the cut will be located at 26.0 inches.
Examples
Imagine you're baking a cake and need to divide the batter into two pans in a 2:3 ratio. If you have a measuring cup that starts with a 2-inch mark due to a manufacturing defect, you need to calculate where to pour the batter to achieve the correct ratio. This problem helps you determine the exact point to pour the batter, ensuring the cake layers have the desired proportions. Understanding ratios and applying them in practical situations like baking ensures consistent and delicious results.
Genevieve will cut the ribbon at 26.0 inches from the starting point after the frayed end, using the ratio of 2:3. The calculations show that she will need to cut at this specific point to maintain the ratio for the rest of the ribbon. Therefore, the final answer is 26.0 inches.
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