Two stores sell CDs in packages, as shown in the table below.
CD Prices at Store A
Number of CDs in Package
1
12
20
45
Cost
$0.70
$8.40
?
$31.50
CD Prices at Store B
Number of CDs in Package
1
20
30
65
Cost
$0.60
?
$18.00
$39.00
If the rate at each store is constant, which statement correctly compares the cost of a package containing 20 CDs?
The cost at Store A is $2.00 greater than at Store B.
The cost at Store B is $2.00 greater than at Store A.
The cost at Store A is $1.00 greater than at Store B.
The cost at Store B is $1.00 greater than at Store A.
To compare the cost of a package containing 20 CDs at Store A and Store B, we can refer to the given data in the table.
At Store A, the cost for a package of 12 CDs is $8.40. This means that the cost for each CD is $8.40/12 = $0.70.
So, the cost for a package of 20 CDs at Store A would be: 20 CDs * $0.70/CD = $14.00.
At Store B, the cost for a package of 30 CDs is $18.00. This means that the cost for each CD is $18.00/30 = $0.60.
So, the cost for a package of 20 CDs at Store B would be: 20 CDs * $0.60/CD = $12.00.
Comparing the two costs, we can see that the cost at Store A ($14.00) is $2.00 greater than the cost at Store B ($12.00).
Therefore, the correct statement is: The cost at Store A is $2.00 greater than at Store B.
T-Shirts R Us advertises shirts as shown below.
3 white shirts and 2 black shirts are 10 dollars per shirt.
Which quantities in the advertisement represent a unit rate?
3 white shirts to 2 black shirts
2 black shirts for every 5 shirts
$10 per shirt
$50 per shirt
A unit rate is a rate that compares a quantity to a single unit. The unit rate allows us to determine the cost or value of one unit.
In the given advertisement, the unit rate is represented by "$10 per shirt". This tells us that each individual shirt costs $10.
The other quantities do not represent unit rates. For example, "3 white shirts to 2 black shirts" is a ratio that does not provide a rate per unit. Similarly, "2 black shirts for every 5 shirts" is a ratio that does not represent a specific cost per unit. "$50 per shirt" is not a unit rate either, as it indicates a higher cost than the actual rate given in the advertisement.
A van can travel 18 miles on each gallon of gasoline. At that rate, how many miles can the van travel on 15 gallons of gasoline?
33 miles
83 miles
120 miles
270 miles
To find out how many miles the van can travel on 15 gallons of gasoline, we need to multiply the number of gallons by the rate of miles per gallon.
Given that the van can travel 18 miles on each gallon of gasoline, we can calculate the total miles the van can travel on 15 gallons by multiplying 18 miles/gallon by 15 gallons.
Miles = (Miles per gallon) * (Gallons)
Miles = 18 * 15
Miles = 270
Therefore, the van can travel 270 miles on 15 gallons of gasoline.
So, the correct answer is 270 miles.
A car travels 22 miles for every gallon of gasoline used. The table below represents this relationship.
Gas Mileage
Distance Traveled
(miles)
Gasoline Used
(gallons)
22
1
44
2
x
3
88
4
Which equation correctly shows a pair of equivalent ratios that can be used to find the unknown?
StartFraction 1 over 22 EndFraction = StartFraction x over 2 EndFraction
StartFraction 22 over 1 EndFraction = StartFraction x over 2 EndFraction
StartFraction 1 over 22 EndFraction = StartFraction x over 3 EndFraction
StartFraction 22 over 1 EndFraction = StartFraction x over 3 EndFraction
To find the equation that correctly represents a pair of equivalent ratios, we need to compare the distance traveled (miles) to the gasoline used (gallons) in each case.
The given information tells us that the car travels 22 miles for every gallon of gasoline used. So, for the ratio involving the unknown, we also need to use 22 as the value for distance traveled.
Let's analyze the options:
Option 1: StartFraction 1 over 22 EndFraction = StartFraction x over 2 EndFraction
This equation does not match the given information because it uses 1 as the distance traveled, instead of 22.
Option 2: StartFraction 22 over 1 EndFraction = StartFraction x over 2 EndFraction
This equation correctly represents a pair of equivalent ratios. It states that 22 miles is equivalent to x number of gallons when the car travels 2 miles per gallon. However, this equation does not match the given information, which states that the car travels 22 miles per gallon.
Option 3: StartFraction 1 over 22 EndFraction = StartFraction x over 3 EndFraction
This equation does not match the given information because it uses 3 as the distance traveled, instead of 22.
Option 4: StartFraction 22 over 1 EndFraction = StartFraction x over 3 EndFraction
This equation correctly represents a pair of equivalent ratios. It states that 22 miles is equivalent to x number of gallons when the car travels 3 miles per gallon. This equation matches the given information.
Therefore, the correct equation is: StartFraction 22 over 1 EndFraction = StartFraction x over 3 EndFraction
A glacier is moving at a rate of 0.3 inches every hour. The table below represents this relationship.
Glacial Movement
Distance Moved (inches)
Time
(hours)
0.3
1
0.6
2
0.9
3
x
4
What value of x completes the table?
1.2
1.5
3.6
13.3
To determine the value of x that completes the table, we need to analyze the relationship between distance moved (inches) and time (hours), keeping in mind that the glacier is moving at a rate of 0.3 inches every hour.
If we observe the table, we can see that the distance moved doubles for each hour that passes. So, for each hour, the distance moved increases by 0.3 inches.
Let's calculate the distance moved for 4 hours:
Distance moved for 1 hour: 0.3 inches
Distance moved for 2 hours: 0.3 inches + 0.3 inches = 0.6 inches
Distance moved for 3 hours: 0.6 inches + 0.3 inches = 0.9 inches
Now, to find the distance moved for 4 hours:
Distance moved for 4 hours: 0.9 inches + 0.3 inches = 1.2 inches
Therefore, the value of x that completes the table is 1.2 inches.
So, the correct answer is 1.2 inches.
The table below shows the cost of bananas at a local grocery store.
Banana Prices
Weight of Bananas
(pounds)
Cost
($)
1
0.75
2
1.50
3
2.25
4
3.00
?
3.75
How many pounds of bananas cost $3.75?
5
6
7
8
To determine the number of pounds of bananas that cost $3.75, we need to look for the missing value in the table.
By analyzing the given data in the table, we can see that the cost of bananas is increasing proportionally with the weight of bananas.
Let's calculate the cost per pound of bananas based on the known values in the table:
For 1 pound of bananas, the cost is $0.75.
So, the cost per pound is $0.75/1 pound = $0.75.
To find the missing value, we can divide the given cost of $3.75 by the calculated cost per pound:
$3.75 / $0.75/pound = 5 pounds.
Therefore, 5 pounds of bananas cost $3.75.
So, the correct answer is 5.
Caleb types 100 words in 5 minutes. What is the unit rate?
100 words to 5 minutes
5 minutes per 100 words
20 words per minute
1 minute to 20 words
To find the unit rate, we need to determine the rate for a single unit. In this case, we want to find the rate of words per minute.
Given that Caleb types 100 words in 5 minutes, the unit rate would be the number of words per minute.
To calculate the unit rate, we divide the total number of words typed (100) by the total time taken (5 minutes):
Unit rate = 100 words / 5 minutes = 20 words per minute
Therefore, the unit rate is 20 words per minute.
So, the correct answer is "20 words per minute."
A pound of raisins costs $2.00, and a pound of almonds costs $5.00. Six pounds of a trail mix contains 2 more pounds of raisins than almonds. What is the cost of the 6 pounds of trail mix?
$7.00
$18.00
$24.00
$42.00
To find the cost of 6 pounds of trail mix, we need to determine the cost of the raisins and almonds separately, and then add them together.
Given that a pound of raisins costs $2.00 and a pound of almonds costs $5.00, we can calculate:
Cost of raisins per pound: $2.00
Cost of almonds per pound: $5.00
The total weight of the trail mix is 6 pounds.
The trail mix has 2 more pounds of raisins than almonds. So, if we have x pounds of almonds, the number of pounds of raisins is x + 2 pounds.
Accordingly, we can set up an equation:
x + (x + 2) = 6
Combining like terms:
2x + 2 = 6
Subtracting 2 from both sides:
2x = 4
Dividing both sides by 2:
x = 2
So, we have 2 pounds of almonds and (2 + 2) = 4 pounds of raisins.
The cost of 2 pounds of almonds is: 2 pounds * $5.00/pound = $10.00
The cost of 4 pounds of raisins is: 4 pounds * $2.00/pound = $8.00
Adding these costs together:
$10.00 + $8.00 = $18.00
Therefore, the cost of the 6 pounds of trail mix is $18.00.
So, the correct answer is $18.00.