Question

A County Superintendent of Highways is interested in the numbers of different types of vehicles that regularly travel within his county. In the month of August, a total of 192 registrations were purchased for passenger cars and pickup trucks at the local Department of Motor Vehicles (DMV). The DMV reported that in the month of August, for every 5 passenger cars registered, there were 7 pickup trucks registered. How many of each type of vehicle were registered in the county in the month of August?
a. Using the information in the problem, write four different ratios and describe the meaning of each.
b. Make a tape diagram that represents the quantities in the part-to-part ratios that you wrote.
c. How many equal-sized parts does the tape diagram consist of?
d. What total quantity does the tape diagram represent?
e. What value does each individual part of the tape diagram represent?
f. How many of each type of vehicle were registered in August?

Answer 1

Answer:

a) The ratio of passenger cars to pickup trucks is $\frac{5}{7}$

The ratio of pickup trucks to passenger cars is $\frac{7}{5}$

The ratio of passenger cars to total vehicles is $\frac{5}{12}$

The ratio of pickup trucks to total vehicles is $\frac{7}{12}$

b) The tape diagram is shown in the attached picture.

c) The tape diagram has 12 equal-sized parts.

d) The total quantity that the tape diagram represent is 192.

e) The value of each individual part of the tape is 16.

f) There were registered 80 passenger cars and 112 pickup trucks.

Step-by-step explanation:

a) According to the information in the problem, that for every 5 passenger cars registered, there were 7 pickup trucks registered.

So the ratios are:

Passenger cars to pickup trucks: $\frac{5}{7}$

Pickup trucks to passenger cars: $\frac{7}{5}$

If we calculate the total vehicles: 5+7=12

So, we can get two ratios more:

Passenger cars to total vehicles is $\frac{5}{12}$

Pickup trucks to total vehicles is $\frac{7}{12}$

b) We make a tape diagram where each box represents a vehicle so we draw 5 boxes for cars and 7 boxes for pickup trucks.

c) If we count the total quantity of boxes, there are 12.

d) This diagram represents the total quantity of registrations in August which is 192.

e) To get the representation of each part of the tape diagram we have to divide 192 by 12. 192÷12=16

f) Finally, we multiply 16 by the number of boxes of each type of vehicle:

Cars: 16×5=80

Pickup trucks: 16×7=112