Questions: Jaime Bailey is chair of a department at a college. Jaime has a budget in which 1/5 of the money is for photocopying, 2/7 of the money is for computer-related expenses, and the rest of the money is for student tutors in the foreign languages lab. What fraction of Jaime's budget is for student tutors? The fraction of Jaime's budget for student tutors is.

$Jaime Bailey is chair of a department at a college. Jaime has a budget in which 1/5 of the money is for photocopying, 2/7 of the money is for computer-related expenses, and the rest of the money is for student tutors in the foreign languages lab. What fraction of Jaime's budget is for student tutors? The fraction of Jaime's budget for student tutors is.$

Transcript text: Jaime Bailey is chair of a department at a college. Jaime has a budget in which $\frac{1}{5}$ of the money is for photocopying, $\frac{2}{7}$ of the money is for computer-related expenses, and the rest of the money is for student tutors in the foreign languages lab. What fraction of Jaime's budget is for student tutors? The fraction of Jaime's budget for student tutors is $\square$

Solution

Solution Steps

To determine the fraction of Jaime's budget allocated for student tutors, we need to subtract the fractions allocated for photocopying and computer-related expenses from the total budget (which is 1).

Calculate the total fraction allocated for photocopying and computer-related expenses.
Subtract this total from 1 to find the fraction for student tutors.

Step 1: Calculate the Fraction for Photocopying

The fraction of the budget allocated for photocopying is given as: \[ \frac{1}{5} \]

Step 2: Calculate the Fraction for Computer-Related Expenses

The fraction of the budget allocated for computer-related expenses is given as: \[ \frac{2}{7} \]

Step 3: Calculate the Total Allocated Fraction

To find the total fraction allocated for both photocopying and computer-related expenses, we add the two fractions: \[ \text{Total Allocated Fraction} = \frac{1}{5} + \frac{2}{7} \] To add these fractions, we find a common denominator, which is 35: \[ \frac{1}{5} = \frac{7}{35}, \quad \frac{2}{7} = \frac{10}{35} \] Thus, \[ \text{Total Allocated Fraction} = \frac{7}{35} + \frac{10}{35} = \frac{17}{35} \]

Step 4: Calculate the Fraction for Student Tutors

The fraction of the budget allocated for student tutors is the remaining fraction after subtracting the total allocated fraction from 1: \[ \text{Fraction for Student Tutors} = 1 - \frac{17}{35} \] Converting 1 to a fraction with a denominator of 35: \[ 1 = \frac{35}{35} \] Thus, \[ \text{Fraction for Student Tutors} = \frac{35}{35} - \frac{17}{35} = \frac{18}{35} \]