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Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.Band students are tested on, and required to pass, a certain number of scales during the year. As of today, Kendra has passed scales, whereas her friend Jackie has passed of them. Going forward, Kendra has committed to passing scales per week, and Jackie has committed to passing per week. At some point soon, the two friends will have passed the same number of scales. How long will that take? How many scales will that be?In weeks, the friends will each have passed scales.
Full solution
Q. Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.Band students are tested on, and required to pass, a certain number of scales during the year. As of today, Kendra has passed scales, whereas her friend Jackie has passed of them. Going forward, Kendra has committed to passing scales per week, and Jackie has committed to passing per week. At some point soon, the two friends will have passed the same number of scales. How long will that take? How many scales will that be?In weeks, the friends will each have passed scales.
- Define Variables: Define the variables for the number of scales Kendra and Jackie have passed.Let's let represent the total number of scales Kendra has passed after a certain number of weeks, and represent the total number of scales Jackie has passed after the same number of weeks.
- Write Equations: Write the equations based on the given information.Kendra starts with scales and passes scales per week. So, , where is the number of weeks.Jackie starts with scales and passes scales per week. So, .
- Set Equations Equal: Set the equations equal to each other to find when Kendra and Jackie will have passed the same number of scales.
- Solve for w: Solve for w by isolating the variable on one side of the equation.
- Total Scales Kendra: Determine the total number of scales passed by Kendra after weeks.K = \(54\)
- Verify Jackie's Scales: Verify the result by checking if Jackie has also passed the same number of scales after \(w\) weeks.\(\newline\)\(J = 3w + 15\)\(\newline\)\(J = 3(13) + 15\)\(\newline\)\(J = 39 + 15\)\(\newline\)J =
- Conclude Solution: Conclude the solution by stating how many weeks it will take and how many scales each will have passed.In weeks, the friends will each have passed scales.
