Go through the Math in Focus Grade 6 Workbook Answer Key Chapter 5 Review Test to finish your assignments.

## Math in Focus Grade 6 Course 1 A Chapter 5 Review Test Answer Key

**Concepts and Skills**

**Solve.**

Question 1.

A factory produces 300 video game disks in 15 minutes. How many video game disks can it produce in 1 minute?

Answer:

20 discs

Explanation:

Video game discs per unit = \(\frac{300}{15}\)

Multiply with common factor on both sides.

Thus, the factory produces 20 discs.

Question 2.

A printer can print 25 pages per minute. At this rate, how long will it take to print 2,000 pages?

Answer:

80 minutes

Explanation:

A printer can print 25 pages per minute = *25 X 4 *= 100.

100 X 20 = *2,000*, and 4 X 20 = 80.

each minute makes *25 pages*, and 4 *min *= 100,

which means that 8 *min *= 2,000 (25 x 8 = 2,000)

**Problem Solving**

**Solve. Show your work.**

Question 3.

An empty bathtub is filled with water at a rate of 2.5 liters per minute. How long will it take to fill the bathtub with 30 liters of water?

Answer:

12 min

Explanation:

Let x = number of minutes

( 2.5 liters/min )X (x) = 30 liters

x = (30 liters) / (2.5 liters/min)

x = 30/2.5 min

x = 12 min

Question 4.

\(\frac{2}{3}\) cup of oatmeal is needed to make 10 granola bars. How many such granola bars can be made with 20 cups of oatmeal?

Answer:

300 bars

Explanation:

10 granola bars can be made from \(\frac{2}{3}\) cups

now we know we have 20 cups of oatmeal,

write as equivalent ratio

2/3 cup oatmeal 20 cups of oatmeal

——————- = ———————

10 granola bars ? granola bars

10 bars/(2/3 cups) = 15 bars/cup

15 bars/cup X (20cup) = 300 bars

Question 5.

150 grams of fertilizer is required for a land area of 6 square meters.

a) At this rate, how many grams of fertilizer are required for a land area of 13 square meters?

Answer:

13 sq m land area

Explanation:

If 150g of fertilizer can cover *6 sq m* of *land* then,

25 *g* of fertilizer can cover 1 *sq m* of *land*;

For *13 sq m* of *land = \(\frac{150}{6}\) ÷ \(\frac{25}{1}\)
*=

*\(\frac{150}{150}\) = 1*

1 gram for 1 sq m land

So, 13 grams for 13 sq m land.

1 gram for 1 sq m land

So, 13 grams for 13 sq m land.

b) For what land area will 850 grams of fertilizer be sufficient?

Answer:

34 sq m land

Explanation:

25g of fertilizer covers 1 sq m of land

So, 850 g of fertilizer sufficient to

= * \(\frac{850}{25}\) = 34*

Question 6.

A machine can stamp 36 bottle caps in 10 seconds. Copy and complete the table.

a) At this rate, how many bottle caps can the machine stamp in 5 minutes?

Answer:

1,080 stamps

Explanation:

A machine can stamp 216 bottles per minute.

In 5 min, machine can stamp

= 216 x 5 = 1,080

b) At this rate, how many minutes will it take to stamp 24,408 bottle caps?

Answer:

406 bottles

Explanation:

1 min = 60 seconds

24,408 *÷ 60 = 406*

Question 7.

The table below shows the charges for using an Internet service.

Nicholas used the Internet service for 16 hours and 40 minutes last month.

a) Under which plan would he have to pay less?

Answer:

Plan A

b) How much less?

Answer: $4

Explanation:

*In Plan A*

price for 10hrs = $6

price for subsequent half hour = $1

Total time used = 16 hours and 40 minutes

price for the fist 10 hours = $6

remaining time = 16-10hrs = 6hrs and 40minutes

No of half hours in 6 hours and 40 minutes = 6 x 2 + 2 = 12 + 2 = 14

price for the half hours = 14 x $1 = 14$

TOTAL PRICE = $6 + $14 = $20.00

*Plan B*

price for 12hrs = $4

price for subsequent half hour = $2

Total time used = 16 hours and 40 minutes

price for the fist 12 hours = $4

remaining time = 16-12hrs = 4hrs and 40minutes

No of half hours in 4 hours and 40 minutes = 4 x 2 + 2 = 8 + 2 = 10

price for the half hours = 10 x $2 = 20$

TOTAL PRICE = $4 + $20 = $24.00

There fore PLAN A is the best plan

Question 8.

Ashley took 3 minutes to run a distance of 540 meters from Point X to Point Y. Grace took 2 minutes to run a distance of 480 meters from Point Z to Point Y.

a) Find the speed of each girl.

Answer:

Ashley speed is 180m per min

Grace speed is 240m per min

Explanation:

Speed = \(\frac{Distance}{Time}\)

Speed = \(\frac{540}{3}\)

Speed =180m per minute

Ashley speed is 180m per min

Speed = \(\frac{Distance}{Time}\)

Speed = \(\frac{480}{2}\)

Speed = 240 m/minute

Grace speed is 240m per min

b) Which of the two girls ran faster?

Answer:

Grace speed is more.

Explanation:

From the above information given,

Speed = \(\frac{480}{2}\)

Speed = 240 m/minute

Grace speed is 240m per min

Question 9.

The distance between Town A and Town B is 45 kilometers.

a) If a train travels at a speed of 60 kilometers per hour, how long will it take to travel from Town A to Town B?

Answer:

45 minutes

Explanation:

If the train travels at 60km/hr,

it travels at 1 km/min.

1km = 1min

45 km = ?

So, it takes 45 min to go from A to B.

b) If a train takes 40 minutes to travel from Town A to Town B, what is its speed in kilometers per minute? Round your answer to 1 decimal place.

Answer:

1.1 km/min

Explanation:

We can find the rate by dividing the Distance by the Time

45km / 40 min = 1.125 km/min

= 1.1 km/min (rounded)

Question 10.

At 7:30 A.M., a bus left Town P for Town Q at a speed of 60 kilometers per hour. 15 minutes later, a car left Town Q and headed for Town P. The car reached Town P at 10:45 A.M. The bus reached Town Q at noon.

a) What is the distance between Town P and Town Q?

Answer:

270 km

Explanation:

The bus took 4.5 hrs, with speed 60kph town P to town Q

Distance = Speed x Time

= 60 x 4.5

=270 kilometers

b) What was the speed of the car?

Answer:

90 kph

Explanation:

a car started at 7:45 Town Q and headed for Town P. The car reached Town P at 10:45 A.M.

Time =3 hours

Distance= 270 KM

Speed = \(\frac{Distance}{Time}\)

Speed = \(\frac{270}{3}\)

Speed = 90 KMPH

Question 11.

Brian drove 120 miles at speed of 60 miles per hour. He drove the same distance back home at average speed of 40 miles per hour. Brian adds these speeds and divides by 2 to come up with an average speed of 50 miles per hour. What is wrong with his reasoning? Find his average speed.

Answer:

48mph

Explanation:

Time = distance/speed

Joe drives at two different speeds: 60 mph and 40 mph.

Time spent driving 60 mph = 120 miles/60 mph = 2 hours

Time spent driving 40 mph = 120 miles/40 mph = 3 hours

T = t1 + t2 = 5 hours

Average speed = Total Distance/T

= 240/5 = 48mph