Question

Need to make sure my word problem and equation is correct.

Answer 1

Given: Michael earns $150 per day washing cars.

x is the number of hours

y is the number of cars

His hourly wage = $10 per hour

He earns $6 for every car.

so, 10x + 6y = 150

So, to find the number of hours and the number of cars, we will make a relation between x and y

Both x and y is greater than 0

As shown, the answer will be the line segment between the points

( 0, 25 ) and ( 15, 0 )

So, one solution is ( 3, 20 )

so, he can work for 3 hours, during it can wash 20 cars

The other possible solutions are:

( 6, 15 ) , ( 9, 10 )

we will write the equation: 10x + 6y = 150

In slope intercept form as follows:

$10x+6y=150$

subtract ( 10x ) from both sides:

$\begin{gathered} -10x+10x+6y=-10x+150 \\ 6y=-10x+150 \end{gathered}$

divide both sides by 6

$\begin{gathered} y=-\frac{10}{6}x+\frac{150}{6} \\ \\ y=-\frac{5}{3}x+25 \end{gathered}$