ACT MATHEMATICS QUESTION

Question

The weekly fee for staying at the Pleasant Lake Campground is $20 per vehicle and $10 per person. Last year, weekly fees were paid for v vehicles and p persons. Which of the following expressions gives the total amount, in dollars, collected for weekly fees last year?

A. 20v + 10p

B. 20p + 10v

C. 10(v + p)

D. 30(v + p)

E. 10(v + p) + 20p

Answer 1

Which once has 20v and 10p?

Answer 2

The weekly fee for staying at the Pleasant Lake Campground is $20 per vehicle and $10 per person. Last year, weekly fees were paid for v vehicles and p persons. Which of the following expressions gives the total amount, in dollars, collected for weekly fees last year?

A. 20v + 10p

B. 20p + 10v

C. 10(v + p)

D. 30(v + p)

E. 10(v + p) + 20p

Read the question carefully, it states that 20 dollars per vehicle (v) and 10 dollars per person (p). So the answer is the total number of vehicles times 20 dollars plus the total number of people times 10 dollars.

So, the answer is 20v + 10p.

Answer 3

There are two ways to approach this kind of question:

a) The "I hate algebra" approach

b) The "I like algebra, but word questions are tough" approach

*c) The hybrid approach

a) Let's start with the "No-Algebra" approach to this algebra question!

The question is charging per vehicle and per person, so come up a number of vehicles (above 2, because they set up traps!) and a number of people. Think about reasonable numbers.

For example, let's say 12 people are going camping, and they are arriving in 3 vehicles.

Before we go any further, let's write down what we have set p and v to:

p = 12

v = 3

At this point, you will go through each answer and calculate the value using 12 for p, and 3 for v, and write the value next to each answer choice.

Now we figure out the costs:

How much does it cost for 3 vehicles to enter?

3 x $20 = $60

Now how much does it cost for all 12 people?

12 x $10 = $120

So what is the total cost for all of the vehicles and people? Notice, we have converted both of these to $ dollars, so we can just add the costs:

$120 + $60 = $180

So we go back the the labeled answers and circle the one that gave you $180

Note: If the numbers you use provide 2 answers that are the same, you made need to pick different numbers. It's often best to avoid using 0, 1, or 2.

b) I like algebra, but word problems are tough!

We can think about this logically like the above explanation, but instead of solving through the answer, we can set this up algebraically using the units.

p represents the cost per person or, $ / persons

we want to get cost in the end, and we need persons to cancel out: persons x ($ / persons) = $

The same applies to v: cost per vehicle is $ / vehicle; vehicles x ($ / vehicle) = $

Once they both share the same units, $, they can be added.

c) A hybrid approach - you can test out the numbers to verify that the values you are multiplying make sense before deciding what variable multiplies by the 10 and the 20, and then algebraically construct an answer.

Answer 4

A good way to think about this is in terms of the units--the quantities used to measure something.

The problem gives you a lot of numbers, but these numbers have units, which will make it easier to solve.

Here are our quantities:

20 dollars per vehicle

10 dollars per person

v vehicles that visited the park last year

p people that visited the park last year

To find the number of dollars made on a certain thing (vehicles or people), we multiply:

p persons x (10 dollars/person)

You can treat units like numbers or variables, and cross them out. In the expression above, the "person" cancels out, and you end up with

10p dollars

The same thing works for the vehicles:

v vehicles x 20 dollars/vehicle = 20v dollars

We want the total amount of dollars that the park made on vehicles and people last year. In word problems, "total" usually means you're going to use addition. Add the money the park made on vehicles to the money that it made on people:

20v+10p