1.A machine can fill 5,400 bottles in 3 hours. How many bottles can it fill in 8 hours?
2.In 4 hours, a comet that is far from the sun usually travels 8,000 miles. How far will the comet travel in 10 hours?(1 point)
3.Suppose contact lenses cost $300 for a year’s supply or $30 for a month’s supply. Which is less expensive to order per year, paying for 12 months at one time or paying for 1 month at a time?(1 point)
4.Jon is trying to decide where to buy discounted movie tickets. Costless sells a pack of 10 tickets for $70, and the website, Movies Unlimited, sells them at 8 tickets for $60. What is the unit price at each company? (1 point)
5.It rained 464 inches in the rainforest in the last 2 years. On average, how much rain fell in 1 year?(1 point)
6.Volunteers put together 40 school-supply kits in 8 minutes. At this rate, how many could they put together in 30 minutes? Solve this problem using a unit rate. (1 point)
Responses
6 school-supply kits
6 school-supply kits
150 school-supply kits
150 school-supply kits
10.67 school-supply kits
10.67 school-supply kits
9,600 school-supply kits
7.A subscription to Time magazine is $24.97 for one year, $45.94 for two years, or $74.91 for three years. Which plan is least expensive if you want the subscription per year? Solve this problem using unit price.(1 point)
Responses
The plans are the same price for two years.
The plans are the same price for two years.
$45.94 for two years
$45.94 for two years
$24.97 for one year
$24.97 for one year
$74.91 for three years
8.At the grocery store, one brand of ice cream costs $4.50 for 48 ounces. The same brand costs $7 for 128 ounces or $3 for 64 ounces. Which size has the lower unit price?(1 point)
Responses
48 ounces
48 ounces
They cost the same per ounce.
They cost the same per ounce.
128 ounces
128 ounces
64 ounces
9.An oil spill covers 4 square kilometers in 1/4 of an hour. At this rate, how many square kilometers will it cover in 2 hours?(1 point)
Responses
8 square kilometers
8 square kilometers
32 square kilometers
32 square kilometers
16 square kilometers
16 square kilometers
2 square kilometers
10.A scientist samples a deer population and finds 200 deer in an area of 10 square miles. On average, how many deer can the scientist expect to find in an area of 300 square miles?(1 point)
Responses
6,000 deer
6,000 deer
320 deer
320 deer
20 deer
20 deer
60,000 deer
The correct answers are:
1. A machine can fill 5,400 bottles in 3 hours, so in 8 hours it can fill (5,400/3)*8 = 14,400 bottles.
2. In 4 hours, the comet travels 8,000 miles, so in 10 hours it will travel (8,000/4)*10 = 20,000 miles.
3. The cost for a year's supply of contact lenses is $300, which is less expensive than paying for 12 months at one time, which would be (12*$30) = $360.
4. Costless sells a pack of 10 tickets for $70, so the unit price is ($70/10) = $7 per ticket. Movies Unlimited sells a pack of 8 tickets for $60, so the unit price is ($60/8) = $7.50 per ticket. Therefore, Costless has the lower unit price.
5. It rained 464 inches in 2 years, so on average, in 1 year it would rain (464/2) = 232 inches.
6. Volunteers can put together 40 school-supply kits in 8 minutes, so at this rate, in 30 minutes they could put together (40/8)*30 = 150 school-supply kits.
7. The subscription to Time magazine is $24.97 for one year, so the unit price per year is $24.97. The unit price for two years is ($45.94/2) = $22.97. The unit price for three years is ($74.91/3) = $24.97. Therefore, the one-year plan is least expensive.
8. The unit price for the 48-ounce ice cream is ($4.50/48) = $0.0938 per ounce. The unit price for the 128-ounce ice cream is ($7/128) = $0.0547 per ounce. The unit price for the 64-ounce ice cream is ($3/64) = $0.0469 per ounce. Therefore, the 64-ounce size has the lower unit price.
9. An oil spill covers 4 square kilometers in 1/4 of an hour, so at this rate, in 2 hours it will cover (4/1/4)*2 = 32 square kilometers.
10. The scientist samples 200 deer in 10 square miles, so on average, in 300 square miles the scientist can expect to find (200/10)*300 = 6,000 deer.
1. To find the number of bottles that can be filled in 8 hours, you can use a proportion.
Since the machine can fill 5,400 bottles in 3 hours, the rate would be 5,400 bottles / 3 hours = 1,800 bottles per hour.
So, in 8 hours, the machine can fill 1,800 bottles/hour * 8 hours = 14,400 bottles.
2. If the comet travels 8,000 miles in 4 hours, you can use a proportion to find how far it will travel in 10 hours.
The rate would be 8,000 miles / 4 hours = 2,000 miles per hour.
So, in 10 hours, the comet will travel 2,000 miles/hour * 10 hours = 20,000 miles.
3. To determine which is less expensive to order per year, paying for 12 months at one time or paying for 1 month at a time, you can compare the total cost for both options.
The cost for a year's supply would be $300, while the cost for a month's supply would be $30 * 12 months = $360.
Therefore, paying for 12 months at one time is less expensive.
4. To find the unit price at each company, divide the total cost of the tickets by the number of tickets.
For Costless, the unit price would be $70 / 10 tickets = $7 per ticket.
For Movies Unlimited, the unit price would be $60 / 8 tickets = $7.50 per ticket.
Therefore, the unit price at Costless is $7 and the unit price at Movies Unlimited is $7.50.
5. To find the average amount of rain that fell in 1 year, divide the total amount of rain by the number of years.
The average amount of rain that fell in 1 year would be 464 inches / 2 years = 232 inches.
6. To find out how many school-supply kits can be put together in 30 minutes, you can use a unit rate.
Since volunteers put together 40 school-supply kits in 8 minutes, the rate would be 40 kits / 8 minutes = 5 kits per minute.
So, in 30 minutes, the volunteers could put together 5 kits/minute * 30 minutes = 150 school-supply kits.
7. To determine which plan is least expensive if you want the subscription per year, you need to calculate the unit price for each plan.
For the one-year subscription, the unit price would be $24.97 / 1 year = $24.97 per year.
For the two-year subscription, the unit price would be $45.94 / 2 years = $22.97 per year.
For the three-year subscription, the unit price would be $74.91 / 3 years = $24.97 per year.
Therefore, the two-year subscription plan is least expensive per year.
8. To find which size has the lower unit price, divide the cost by the number of ounces for each size.
For the 48-ounce size, the unit price would be $4.50 / 48 ounces = $0.09375 per ounce.
For the 128-ounce size, the unit price would be $7 / 128 ounces = $0.05469 per ounce.
For the 64-ounce size, the unit price would be $3 / 64 ounces = $0.04688 per ounce.
Therefore, the 64-ounce size has the lower unit price.
9. To find out how many square kilometers the oil spill will cover in 2 hours, you can use a proportion.
Since the oil spill covers 4 square kilometers in 1/4 of an hour, the rate would be 4 square kilometers / (1/4 hour) = 4 * 4 = 16 square kilometers per hour.
So, in 2 hours, the oil spill will cover 16 square kilometers/hour * 2 hours = 32 square kilometers.
10. To determine how many deer the scientist can expect to find in an area of 300 square miles, you can use a proportion.
Since the scientist found 200 deer in an area of 10 square miles, the rate would be 200 deer / 10 square miles = 20 deer per square mile.
So, in an area of 300 square miles, the scientist can expect to find 20 deer/square mile * 300 square miles = 6,000 deer.