Question

part 5: word problems using algebra
score: 66.67/100 answered: 7/10
question 9
a mechanic completes 30 inspections, which is 75% of the total number of inspections to complete.
write an equation to calculate x number of total inspections to complete.
how many total inspections must be completed? \boxed{} inspections
how many inspections does the mechanic have left to complete? \boxed{} inspections

Explanation:

First Sub - Question: Write an equation

Step1: Define the relationship

75% of the total inspections \( x \) is equal to 30. We know that 75% can be written as \( 0.75 \) or \( \frac{75}{100}=\frac{3}{4} \). So the equation is based on the fact that a percentage of a number is equal to another number.
\( 0.75x = 30 \) (or \( \frac{3}{4}x=30 \))

Second Sub - Question: Find total inspections

Step1: Solve the equation \( 0.75x = 30 \)

To solve for \( x \), we divide both sides of the equation by \( 0.75 \).
\( x=\frac{30}{0.75} \)

Step2: Calculate the value

\( \frac{30}{0.75}=40 \)

Third Sub - Question: Find inspections left

Step1: Subtract completed from total

We know the total number of inspections is 40 and the number of completed inspections is 30. So we subtract 30 from 40.
\( 40 - 30=10 \)

Answer:

• Equation: \( 0.75x = 30 \) (or \( \frac{3}{4}x = 30 \))
• Total inspections: 40 inspections
• Inspections left: 10 inspections