Jack charges $40 initial fee plus $30 an hour to work on vehicles. mark charges $25 an hour with a $50 initial fee. to work on vehicles. at what number of hours do they charge the same amount? how much is this amount?

write the system.

Step-by-step explanation:

A.)

Let the equal number of hours be represented by variable h;

The two equations will be as follows;

Jack; 40 +30h

Mark; 50 +25h

Next, equate them;

40 + 30h= 50 + 25h

30h - 25h = 50 - 40

5h = 10

h =10/5

h = 2

Therefore, they charge the same amount at 2 hrs.

B.) The amount charged;

Replace the variable H in any of the two equations above with 2 to solve for the amount.

Equation 40+30h = 40 + (30*2)

=40 + 60

= $100

b.) 160 miles on a 5 gallons car

step-by-step explanation:

240/10=24 miles/gallon

160/5=32 miles/gallon

30/1=30 miles/gallon

168/6= 28 miles/gallon

32 miles/gallon is the most amount, so this is the best.

answer: solve 5\cdot 2^x=2405⋅2  

x

=2405, dot, 2, start superscript, x, end superscript, equals, 240.

solution

to solve for xxx, we must first isolate the exponential part. to do this, divide both sides by 555 as shown below. we do not multiply the 555 and the 222 as this goes against the order of operations!

\begin{aligned} 5\cdot 2^x& =240 2^x& =48 \\ \end{aligned}  

5⋅2  

x

2  

x

​    

=240

=48

​

step-by-step explanation: