Math / Numbers & Operations

Question9 Express each of the following as a simplified rate. a 180 students on 3 buses b $\$ 5.60$ for 4 kg c 186 km in $2 \frac{1}{2}$ hours $5: 2$
10 Find the average rate for each situation. a Thelma drove 8000 km in 50 days b Callum saved $\$ 1250$ in 6 months c. Ainslie grew 20 cm in $2 \frac{1}{2}$ years
11 Who earns the most, and by how much, if Kelly is paid $\$ 96570$ a year and Todd earns $\$ 7985$ each month?
Which is faster $70 \mathrm{~km} / \mathrm{h}$ or $21 \mathrm{~m} / \mathrm{s}$ ?

Studdy Solution

STEP 1

1. We are asked to express given quantities as simplified rates.
2. We need to find average rates for given situations.
3. We need to compare earnings to determine who earns more.
4. We need to compare speeds in different units to determine which is faster.

STEP 2

1. Simplify given rates.
2. Calculate average rates.
3. Compare earnings.
4. Compare speeds.

STEP 3

a. Simplify the rate of students per bus.
$\frac{180 \text{ students}}{3 \text{ buses}} = \frac{180}{3} = 60 \text{ students per bus}$

STEP 4

b. Simplify the rate of dollars per kilogram.
$\frac{\$5.60}{4 \text{ kg}} = \frac{5.60}{4} = \$1.40 \text{ per kg}$

STEP 5

c. Simplify the rate of kilometers per hour.
Convert $2 \frac{1}{2}$ hours to an improper fraction: $2.5$ hours.
$\frac{186 \text{ km}}{2.5 \text{ hours}} = \frac{186}{2.5} = 74.4 \text{ km per hour}$

STEP 6

d. Simplify the ratio $5:2$ .
The ratio $5:2$ is already in its simplest form.

STEP 7

a. Find the average rate of kilometers per day for Thelma.
$\frac{8000 \text{ km}}{50 \text{ days}} = \frac{8000}{50} = 160 \text{ km per day}$

STEP 8

b. Find the average rate of dollars saved per month for Callum.
$\frac{\$1250}{6 \text{ months}} = \frac{1250}{6} \approx \$208.33 \text{ per month}$

STEP 9

c. Find the average rate of growth per year for Ainslie.
Convert $2 \frac{1}{2}$ years to an improper fraction: $2.5$ years.
$\frac{20 \text{ cm}}{2.5 \text{ years}} = \frac{20}{2.5} = 8 \text{ cm per year}$

STEP 10

Compare Kelly's and Todd's earnings.
Kelly earns $\$96570$ per year.
Todd earns $\$7985$ per month, so annually he earns:
$\$7985 \times 12 = \$95820$
Kelly earns more than Todd by:
$\$96570 - \$95820 = \$750$

STEP 11

Compare speeds of $70 \text{ km/h}$ and $21 \text{ m/s}$ .
Convert $70 \text{ km/h}$ to meters per second:
$70 \text{ km/h} = \frac{70 \times 1000}{3600} \approx 19.44 \text{ m/s}$
Since $21 \text{ m/s}$ is greater than $19.44 \text{ m/s}$ , $21 \text{ m/s}$ is faster.
The solutions are:
1. Simplified rates: - $60$ students per bus - $\$1.40$ per kg - $74.4$ km per hour - Ratio $5:2$
2. Average rates: - $160$ km per day - $\$208.33$ per month - $8$ cm per year
3. Kelly earns more than Todd by $\$750$ .
4. $21 \text{ m/s}$ is faster than $70 \text{ km/h}$ .

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Studdy Solution

STEP 1

1. We are asked to express given quantities as simplified rates.
2. We need to find average rates for given situations.
3. We need to compare earnings to determine who earns more.
4. We need to compare speeds in different units to determine which is faster.

STEP 2

1. Simplify given rates.
2. Calculate average rates.
3. Compare earnings.
4. Compare speeds.

STEP 3

a. Simplify the rate of students per bus.
$\frac{180 \text{ students}}{3 \text{ buses}} = \frac{180}{3} = 60 \text{ students per bus}$

STEP 4

b. Simplify the rate of dollars per kilogram.
$\frac{\$5.60}{4 \text{ kg}} = \frac{5.60}{4} = \$1.40 \text{ per kg}$

STEP 5

c. Simplify the rate of kilometers per hour.
Convert $2 \frac{1}{2}$ hours to an improper fraction: $2.5$ hours.
$\frac{186 \text{ km}}{2.5 \text{ hours}} = \frac{186}{2.5} = 74.4 \text{ km per hour}$

STEP 6

d. Simplify the ratio $5:2$ .
The ratio $5:2$ is already in its simplest form.

STEP 7

a. Find the average rate of kilometers per day for Thelma.
$\frac{8000 \text{ km}}{50 \text{ days}} = \frac{8000}{50} = 160 \text{ km per day}$

STEP 8

b. Find the average rate of dollars saved per month for Callum.
$\frac{\$1250}{6 \text{ months}} = \frac{1250}{6} \approx \$208.33 \text{ per month}$

STEP 9

c. Find the average rate of growth per year for Ainslie.
Convert $2 \frac{1}{2}$ years to an improper fraction: $2.5$ years.
$\frac{20 \text{ cm}}{2.5 \text{ years}} = \frac{20}{2.5} = 8 \text{ cm per year}$

STEP 10

Compare Kelly's and Todd's earnings.
Kelly earns $\$96570$ per year.
Todd earns $\$7985$ per month, so annually he earns:
$\$7985 \times 12 = \$95820$
Kelly earns more than Todd by:
$\$96570 - \$95820 = \$750$

STEP 11

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Studdy Solution

STEP 1

1. We are asked to express given quantities as simplified rates.2. We need to find average rates for given situations.3. We need to compare earnings to determine who earns more.4. We need to compare speeds in different units to determine which is faster.

STEP 2

1. Simplify given rates.2. Calculate average rates.3. Compare earnings.4. Compare speeds.

STEP 3

a. Simplify the rate of students per bus.180 students3 buses=1803=60 students per bus\frac{180 \text{ students}}{3 \text{ buses}} = \frac{180}{3} = 60 \text{ students per bus}3 buses180 students​=3180​=60 students per bus

STEP 4

b. Simplify the rate of dollars per kilogram.$5.604 kg=5.604=$1.40 per kg\frac{\$5.60}{4 \text{ kg}} = \frac{5.60}{4} = \$1.40 \text{ per kg}4 kg$5.60​=45.60​=$1.40 per kg

STEP 5

c. Simplify the rate of kilometers per hour.Convert 2122 \frac{1}{2}221​ hours to an improper fraction: 2.52.52.5 hours.186 km2.5 hours=1862.5=74.4 km per hour\frac{186 \text{ km}}{2.5 \text{ hours}} = \frac{186}{2.5} = 74.4 \text{ km per hour}2.5 hours186 km​=2.5186​=74.4 km per hour

STEP 6

d. Simplify the ratio 5:25:25:2.The ratio 5:25:25:2 is already in its simplest form.

STEP 7

a. Find the average rate of kilometers per day for Thelma.8000 km50 days=800050=160 km per day\frac{8000 \text{ km}}{50 \text{ days}} = \frac{8000}{50} = 160 \text{ km per day}50 days8000 km​=508000​=160 km per day

STEP 8

b. Find the average rate of dollars saved per month for Callum.$12506 months=12506≈$208.33 per month\frac{\$1250}{6 \text{ months}} = \frac{1250}{6} \approx \$208.33 \text{ per month}6 months$1250​=61250​≈$208.33 per month

STEP 9

c. Find the average rate of growth per year for Ainslie.Convert 2122 \frac{1}{2}221​ years to an improper fraction: 2.52.52.5 years.20 cm2.5 years=202.5=8 cm per year\frac{20 \text{ cm}}{2.5 \text{ years}} = \frac{20}{2.5} = 8 \text{ cm per year}2.5 years20 cm​=2.520​=8 cm per year

STEP 10

Compare Kelly's and Todd's earnings.Kelly earns $96570\$96570$96570 per year.Todd earns $7985\$7985$7985 per month, so annually he earns:$7985×12=$95820\$7985 \times 12 = \$95820$7985×12=$95820Kelly earns more than Todd by:$96570−$95820=$750\$96570 - \$95820 = \$750$96570−$95820=$750

STEP 11

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Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

1. We are asked to express given quantities as simplified rates.
2. We need to find average rates for given situations.
3. We need to compare earnings to determine who earns more.
4. We need to compare speeds in different units to determine which is faster.

1. Simplify given rates.
2. Calculate average rates.
3. Compare earnings.
4. Compare speeds.

a. Simplify the rate of students per bus.
$\frac{180 \text{ students}}{3 \text{ buses}} = \frac{180}{3} = 60 \text{ students per bus}$

b. Simplify the rate of dollars per kilogram.
$\frac{\$5.60}{4 \text{ kg}} = \frac{5.60}{4} = \$1.40 \text{ per kg}$

c. Simplify the rate of kilometers per hour.
Convert $2 \frac{1}{2}$ hours to an improper fraction: $2.5$ hours.
$\frac{186 \text{ km}}{2.5 \text{ hours}} = \frac{186}{2.5} = 74.4 \text{ km per hour}$

d. Simplify the ratio $5:2$ .
The ratio $5:2$ is already in its simplest form.

a. Find the average rate of kilometers per day for Thelma.
$\frac{8000 \text{ km}}{50 \text{ days}} = \frac{8000}{50} = 160 \text{ km per day}$

b. Find the average rate of dollars saved per month for Callum.
$\frac{\$1250}{6 \text{ months}} = \frac{1250}{6} \approx \$208.33 \text{ per month}$

c. Find the average rate of growth per year for Ainslie.
Convert $2 \frac{1}{2}$ years to an improper fraction: $2.5$ years.
$\frac{20 \text{ cm}}{2.5 \text{ years}} = \frac{20}{2.5} = 8 \text{ cm per year}$

Compare Kelly's and Todd's earnings.
Kelly earns $\$96570$ per year.
Todd earns $\$7985$ per month, so annually he earns:
$\$7985 \times 12 = \$95820$
Kelly earns more than Todd by:
$\$96570 - \$95820 = \$750$