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]
Genevieve is cutting a 60-inch piece of ribbon in the ratio of 2:3. 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.
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 = 60 .
Substitute the values into the formula: x = ( 2 + 3 2 ) ( 60 − 2 ) + 2 .
Simplify the expression: x = 5 2 × 58 + 2 = 23.2 + 2 .
Calculate the final cut location: x = 25.2 . The cut will be located at 25.2 inches.
Explanation
Understanding the Formula and Given Information We are given the formula for finding the cut location: x = ( m + n m ) ( x 2 − x 1 ) + x 1 . We need to identify the values for m , n , x 1 , and x 2 from the problem statement.
Identifying the Values From the problem statement, we know that the ribbon is cut in the ratio 2:3, so m = 2 and n = 3 . The ribbon is 60 inches long, and since 2 inches are frayed at one end, the cut starts at 2 inches. Therefore, x 1 = 2 and x 2 = 60 .
Substituting the Values Now, we substitute the values into the formula: x = ( 2 + 3 2 ) ( 60 − 2 ) + 2
Simplifying the Expression Next, we simplify the expression: x = ( 5 2 ) ( 58 ) + 2 x = 5 2 × 58 + 2 x = 5 116 + 2 x = 23.2 + 2 x = 25.2
Final Answer The location of the cut is 25.2 inches.
Examples
Imagine you're baking a cake and need to divide the batter into two pans in a specific ratio to create layers of different thicknesses. The formula used here helps you determine exactly where to divide the batter to achieve the desired ratio. This is also applicable in scenarios like mixing paint to get a specific color blend or dividing resources proportionally in a project.
The cut location for Genevieve's ribbon is found using the formula, resulting in a position of 25.2 inches from the starting point of 2 inches. Therefore, the correct answer is 25.2 in . This is option A.
;
