Ramón rented a sprayer and a generator. On his first job, he used each piece of equipment for 6 hours at a total cost of $90. On his second job, he used the sprayer for 4 hours and the generator for 8 hours at a total cost of $100. What was the hourly cost of each piece of equipment?

The sprayer costs ??$ per hour.

The generator costs ??$ per hour.

and

A hotel charges $20 for the use of its dining room and $2.50 a plate for each dinner. An association gives a dinner and charges $3 a plate but invites four nonpaying guests. If each person has one plate, how many paying persons must attend for the association to collect the exact amount needed to pay the hotel?

a.60

b.44

c.40

d.20

### 1 Answer

OK

Let x = sprayer cost

Let y = generator cost

6x + 6y = 90

4x + 8y = 100 ; mutiply the top by 4 and the bottom by 3

24x + 24y = 360

12x + 24y = 300 ; subtract (the y’s go away)

12x = 60

x = 5

So the sprayer is $5 an hour. Now substitute in the first equation

6(5) + 6y = 90

30 + 6y = 90

6y = 60

y = 10

So the generaltor is $10.

Check in the second equation

4(5) + 8(10) = 100??

20 + 80 = 100?

100 = 100 YES!!

====================

2.5 per plate + 20 to use the room

2.5x + 20 = 3x

20 = .5x

40 = x

Let’s check

2.5 (40) + 20 = $120

3(40) = $120.

So 40 paying guest must attend. The four non-paying guests are not relevant to the question.

Hope that helps.