Question

part 5: word problems using algebra
score: 40/100 answered: 4/10
question 5
an aircraft technician has 31 bolts. the technician needs to replace 7 bolts on each engine.
write an equation to represent ( x ) engines that can be serviced with 31 bolts.
how many engines can be fully serviced with 31 bolts? (think: fully serviced means no partial number of engines is allowed.) engines.
submit question

Explanation:

First Sub - Question (Writing the Equation)

Step1: Identify the relationship

The total number of bolts used for \(x\) engines is the number of bolts per engine times the number of engines. The total number of bolts available is 31. So the equation is based on the fact that the number of bolts used (\(7x\)) should be related to the total bolts (31). The equation representing the situation is \(7x = 31\) (or we can also think in terms of the number of bolts used not exceeding 31, but for writing an equation to represent \(x\) engines serviced with 31 bolts, \(7x=31\) is appropriate as it models the total bolts used for \(x\) engines equal to 31).

Step2: Write the equation

Using the relationship from Step 1, the equation is \(7x = 31\).

Second Sub - Question (Number of Fully Serviced Engines)

Step1: Solve the equation for \(x\)

We have the equation \(7x=31\). To find \(x\), we divide both sides by 7: \(x=\frac{31}{7}\approx4.428\).

Step2: Determine the number of fully serviced engines

Since we can't have a partial number of engines (as per the problem statement), we take the floor of the value of \(x\) (the greatest integer less than or equal to \(x\)). So the number of fully serviced engines is 4.

Answer:

The equation is \(7x = 31\).
The number of engines that can be fully serviced is 4.