Sam wanted to buy candy for all of his friends to share at lunch. One pound of chocolates cost $6.95, but Sam only needs 0.6 of a pound. What will be the total cost for the chocolates Sam buys?
A.
$11.58
B.
$2.78
C.
$4.20
D.
$4.17
We can start by finding the cost of 1 pound of chocolates:
$6.95 ÷ 1 pound = $6.95 per pound
Then, we can multiply that by 0.6 to find the cost of 0.6 pounds:
$6.95 per pound × 0.6 pounds = $4.17
Therefore, the total cost for the chocolates Sam buys is $4.17, which is option D.
Tad and Janice are installing new wood floors in a house. Tad can install 144 square feet of flooring in three hours. Janice can install 576 square feet of flooring in six hours.
How many square feet of flooring can Tad install in eight hours?
square feet
How many square feet of flooring can Janice install in five hours?
square feet
If they each work for 12 hours, how many square feet of flooring can they install?
square feet
How long will it take Pablo to bike 56 miles if he is biking at a speed of 7 mph?
A.
13 hours
B.
3 hours
C.
392 hours
D.
8 hours
We can use the formula distance = rate x time, where distance is 56 miles, rate is 7 mph, and we want to solve for time.
distance = rate x time
56 miles = 7 mph x time
time = 56 miles ÷ 7 mph
time = 8 hours
Therefore, it will take Pablo 8 hours to bike 56 miles at a speed of 7 mph, which is option D.
Complete the rate chart below to find the number of scoops of coffee grounds needed for a certain number of pots of coffee.
Number of Pots of Coffee 3 4 5 6 7
Number of Scoops of Coffee Grounds 9 12 15 18 ?
A.
25
B.
21
C.
23
D.
19
We can see that the ratio of the number of pots of coffee to the number of scoops of coffee grounds is:
3 pots : 9 scoops
4 pots : 12 scoops
5 pots : 15 scoops
6 pots : 18 scoops
To find the number of scoops needed for 7 pots of coffee, we can use the ratio:
5 pots : 15 scoops
7 pots : x scoops
We can set up a proportion using cross products:
5 pots * x scoops = 7 pots * 15 scoops
5x = 105
x = 21
Therefore, the number of scoops of coffee grounds needed for 7 pots of coffee is 21, which is option B.
Find the missing number in the ratio table below.
2 4 6 8
7 14 21 ?
A.
23
B.
26
C.
28
D.
24
We can see that the ratio between the second row and the first row is 7:2. We can use this ratio to find the missing number in the fourth column by multiplying 8 (the number in the first row and fourth column) by the ratio:
7/2 = x/8
We can solve for x by cross multiplying:
2x = 7 * 8
2x = 56
x = 28
Therefore, the missing number in the ratio table is 28, which is option C.
A fruit punch is made by mixing grape juice and apple juice in the ratio of 4 to 2. How many glasses of grape juice and apple juice are needed to make 36 glasses of fruit punch?
The ratio of grape juice to apple juice is 4:2, which can be simplified to 2:1. This means for every 2 units of grape juice, we need 1 unit of apple juice.
We need to find how much of each type of juice we need to make 36 glasses of fruit punch. Let's say we use x as the number of units of grape juice we need. Then, we need half as much apple juice, which is x/2.
The total number of units of juice we need is x + x/2 = 3x/2.
We know that the total number of glasses of fruit punch we need to make is 36. If we assume that each glass contains 1 unit of juice, then we can set up an equation:
3x/2 = 36
To solve for x, we can multiply both sides by 2/3:
x = 24
This means we need 24 units of grape juice and 12 units of apple juice to make 36 glasses of fruit punch.
To check, we can verify that the ratio of grape juice to apple juice is 2:1:
24 ÷ 2 = 12
Therefore, we need 24 glasses of grape juice and 12 glasses of apple juice to make 36 glasses of fruit punch.
Use the table to determine the relationship between liters and milliliters.
Liters Milliliters
1 1,000
2 ?
3 ?
4 ?
Which of the following graphs matches the relationship shown in the table?
W.
X.
Y.
Z.
A.
Z
B.
Y
C.
X
D.
W
The table shows that 1 liter is equal to 1,000 milliliters. To find the number of milliliters in 2, 3, and 4 liters, we can multiply by 1,000:
2 liters = 2,000 milliliters
3 liters = 3,000 milliliters
4 liters = 4,000 milliliters
Therefore, we have the following data points:
(1, 1000), (2, 2000), (3, 3000), (4, 4000)
This shows that the relationship between liters and milliliters is linear, with a slope of 1000 and a y-intercept of 0.
The graph that matches this relationship is graph Z, which is a straight line with a slope of 1000 and a y-intercept of 0.
Therefore, the answer is A. graph Z.
Keisha can make 1 gift basket in 95 minutes. Using this information, complete the table of equivalent ratios to show the number of minutes it takes Keisha to make a certain number of gift baskets.
We can set up a proportion to determine the number of minutes it takes Keisha to make a certain number of gift baskets:
1 gift basket : 95 minutes
2 gift baskets: x minutes
3 gift baskets: y minutes
4 gift baskets: z minutes
To find x, we can use cross-multiplication:
1 x = 2 × 95
x = 190
Therefore, Keisha can make 2 gift baskets in 190 minutes.
To find y, we can again use cross-multiplication:
1 y = 3 × 95
y = 285
Therefore, it would take Keisha 285 minutes to make 3 gift baskets.
Similarly, to find z, we can use cross-multiplication:
1 z = 4 × 95
z = 380
Therefore, Keisha can make 4 gift baskets in 380 minutes.
Using this information, the completed table of equivalent ratios would look like:
Number of Gift Baskets | Number of Minutes
--- | ---
1 | 95
2 | 190
3 | 285
4 | 380
Keisha can make 1 gift basket in 95 minutes. Using this information, complete the table of equivalent ratios to show the number of minutes it takes Keisha to make a certain number of gift baskets.
Gift Baskets 2
4
6
Minutes
380
760
We know that Keisha can make 1 gift basket in 95 minutes.
To find how long it takes her to make 2 gift baskets, we can set up a proportion:
1 gift basket : 95 minutes
2 gift baskets : x minutes
We can use cross-multiplication to solve for x:
1 * x = 2 * 95
x = 190
Therefore, it takes Keisha 190 minutes to make 2 gift baskets.
Similarly, we can set up a proportion to find how long it takes her to make 4 gift baskets:
1 gift basket : 95 minutes
4 gift baskets : x minutes
1 * x = 4 * 95
x = 380
Therefore, it takes Keisha 380 minutes to make 4 gift baskets.
And for 6 gift baskets:
1 gift basket : 95 minutes
6 gift baskets : x minutes
1 * x = 6 * 95
x = 570
Therefore, it takes Keisha 570 minutes to make 6 gift baskets.
Using this information, the completed table of equivalent ratios would be:
Gift Baskets | Minutes
--- | ---
2 | 190
4 | 380
6 | 570
Elijah needed to dig a row along a fence that was 5 feet long. He was able to dig all but 46 inches of the row before dark.
How many inches was he able to dig before dark?
We can start by converting the length of the row to inches. Since 1 foot is equal to 12 inches, we can multiply 5 feet by 12 to get the length of the row in inches:
5 feet * 12 inches/foot = 60 inches
This means the entire row is 60 inches long.
We know that Elijah was able to dig all but 46 inches of the row before dark. To find out how many inches he was able to dig, we can subtract 46 from the total length of the row:
60 inches - 46 inches = 14 inches
Therefore, Elijah was able to dig 14 inches of the row before dark.
A boat moved 39 kilometers in 2 hours.
The boat moved
meters per minute.
The manager of a shopping mall observes how many adults and children enter the food court in one day. He observes whether each customer is an adult or a child.
The manager observes that 675 adults were customers on one particular day, which was 75% of the total customers, t. This is shown in the diagram below.
A percent-tape diagram with number of customers range from 0 to t and percent range 0% to 100% with difference of 25%. Marked 675 adults at 75%.
The total number of customers was
.
The total number of children that were customers was
If 675 adults were 75% of the total customers, we can start by setting up a proportion:
75% = 675 / t
To solve for t, we can cross-multiply:
0.75t = 675
t = 900
Therefore, the total number of customers was 900.
To find the total number of children, we can subtract the number of adults from the total number of customers:
900 - 675 = 225
Therefore, there were 225 children that were customers.
A meal program accepts online payments by way of credit card. For every payment processed, the meal program charges a 2% fee to the customer in addition to their payment amount.
The table below shows payment amounts and the appropriate fees charged.
Payment Amount $
$23.50 $64.00 $
Fee Charged $0.25 $
$
$1.64
To determine the missing fees, we can use the given information about the fee charged: the fee is 2% of the payment amount.
Let's start with the first row of the table. The payment amount is $23.50. To find the fee charged, we can multiply the payment amount by 0.02:
$23.50 x 0.02 = $0.47
Therefore, the fee charged for a $23.50 payment is $0.47.
Moving on to the second row of the table, the fee charged is given as $0.25. We can find the payment amount by setting up a proportion:
2% = $0.25 / payment amount
To solve for the payment amount, we can cross-multiply:
0.02 x payment amount = $0.25
payment amount = $0.25 / 0.02
payment amount = $12.50
Therefore, the payment amount for a $0.25 fee charged is $12.50.
For the third row of the table, the payment amount is $64. To find the fee charged, we can multiply the payment amount by 0.02:
$64 x 0.02 = $1.28
Therefore, the fee charged for a $64 payment is $1.28.
Finally, for the last row of the table, the fee charged is given as $1.64. We can again set up a proportion:
2% = $1.64 / payment amount
0.02 x payment amount = $1.64
payment amount = $1.64 / 0.02
payment amount = $82
Therefore, the payment amount for a $1.64 fee charged is $82.
The completed table with missing values filled in would look like:
Payment Amount | Fee Charged
--- | ---
$23.50 | $0.47
$12.50 | $0.25
$64.00 | $1.28
$82.00 | $1.64
What turns $23.50 into $64
To turn $23.50 into $64, we need to add $40.50.
$23.50 + $40.50 = $64
Therefore, adding $40.50 turns $23.50 into $64.
blank $23.50 then $64.00 and blank
In the given sequence, the first blank is $40.50 and the second blank is not uniquely defined, as there could be many different values for the third number depending on the rules or patterns governing the sequence.
whats the 4th blank to this: blank $23.50 then $64.00 and blank
Without any additional information, we cannot determine the value of the fourth blank. The sequence could continue indefinitely with any number of possible values for the third and subsequent terms, depending on the pattern or rules that govern the sequence.
If 15 is 25% of a value, what is that value?
We can set up a proportion to solve the problem:
15 is 25% of x
25% is the same as 0.25 as a decimal.
So we can write:
15 = 0.25x
To solve for x, we can divide both sides by 0.25:
x = 15 / 0.25
x = 60
Therefore, the value is 60.
If 18 is 45% of a value, what is that value?
We can set up a proportion to solve the problem:
18 is 45% of x
45% is equivalent to 0.45 as a decimal.
So we can write:
18 = 0.45x
To solve for x, we can divide both sides by 0.45:
x = 18 / 0.45
x = 40
Therefore, the value is 40.
To find the rate at which Tad installs flooring, we can divide the number of square feet by the number of hours he works:
144 square feet ÷ 3 hours = 48 square feet per hour
Then, we can use the rate to find how much flooring Tad can install in 8 hours:
48 square feet per hour × 8 hours = 384 square feet
Therefore, Tad can install 384 square feet of flooring in 8 hours.
For Janice, we can find her rate by dividing her number of square feet by her number of hours:
576 square feet ÷ 6 hours = 96 square feet per hour
Then, we can use her rate to find how much flooring she can install in 5 hours:
96 square feet per hour × 5 hours = 480 square feet
Therefore, Janice can install 480 square feet of flooring in 5 hours.
If they each work for 12 hours, we can find the total amount of flooring they install by adding together what each person installs:
Tad: 48 square feet per hour × 12 hours = 576 square feet
Janice: 96 square feet per hour × 12 hours = 1152 square feet
Total: 576 square feet + 1152 square feet = 1728 square feet
Therefore, working together for 12 hours, Tad and Janice can install 1728 square feet of flooring.
We can use the formula rate = distance / time to find the rate of the boat.
Since the boat moved 39 kilometers in 2 hours, we can plug in these values:
rate = 39 km / 2 hours
Simplifying and converting to meters and minutes:
rate = (39 km / 2 hours) * (1000 m / 1 km) * (1 hour / 60 minutes)
rate = 650 meters per minute
Therefore, the boat moved at a rate of 650 meters per minute.