rates and ratios

Question 1

how does the unitary method work?

Answer 1

1. find one unit of a quantity by dividing the amount.
2. multiply the result in step 1 by a number to solve the problem.

Question 2

how are speed (S), time (T) and distance (D) calculated?

Answer 2

S = D ÷ T

T = D ÷ S

D = S x T

Question 3

how is maximum heart rate (MHR) calculated?

Answer 3

MHR = 220 - age (in years)

Question 4

how is target heart rate (THR) calculated?

Answer 4

THR = 65% to 85% of MHR

Question 5

a television uses 80 watts when being used for viewing, and 4 watts when in stand-by mode. if viewed on average for 8 hours per day, and left on stand-by for the remainder of the day, how many kilowatt hours (kWh) are used per day?

Answer 5

       1000

= 0.704 kWh

Question 6

how is fuel consumption calculated?

Answer 6

fuel consumption =
amount of fuel (L) x 100
———————————-
distance travelled (km)

Question 7

a medium-sized car travelled 850km using 78.2L of petrol. what was the fuel consumption?

Answer 7

fuel consumption =
amount of fuel (L) x 100
———————————-
distance travelled (km)

= 78.2 x 100
————–
850

= 9.2L / 100km

Question 8

how is an equivalent ratio found?

Answer 8

equivalent ratios are obtained by multiplying or dividing by the same number.

Question 9

what is the simplest form of the ratio 1.5:3.5?

Answer 9

1.5 x 10 = 15
3.5 x 10 = 35

15 ÷ 5 = 3
35 ÷ 5 = 7

∴ the simplest form of the ratio is 3:7

Question 10

Mikhail and Ilya were given $450 to share in the ratio 4:5. how much money did each person get?

Answer 10

4 + 5 = 9
450 ÷ 9 = $50
50 x 4 = 200
50 x 5 = 250

∴ Mikhail got $200, Ilya got $250

Question 11

how is the scale of a drawing calculated?

Answer 11

scale of a drawing =
drawing length:actual length

Question 12

a scale drawing has a scale of 1:50. find the actual length if the drawing length is 30mm. answer to the nearest centimetre.

Answer 12

actual length = 30 x 50mm
= 1500mm
1500mm ÷ 10
= 150cm

Question 13

a scale drawing has a scale of 1:50. find the drawing length if the actual length is 4.5m. answer to the nearest millimetre.

Answer 13

drawing length = 4.5 ÷ 50m
= 0.09m
0.09m x 1000
= 90mm

Question 14

how is volume (V) calculated?

Answer 14

V = Ah

where V - volume
A - area
h - height

Question 15

what is the trapezoidal rule?

Answer 15

A ≈ w (df + dl)
–
2

where A - area
w - width between the parallel sides
df - distance along the first parallel side
dl - distance along the last parallel side

Question 16

Martin owns a field that is bounded on one side by a curved road. he divides the field into four strips of equal width and records the measurements as 100m total width, with the distances of the parallel sides being 90m, 104m, 105m, 109m and 120m. use the trapezoidal rule to approximate the area of the field.

Answer 16

A ≈ w (df + dl)
–
2

100 ÷ 4 = 25m

A ≈ (25÷2)(90+104) + (25÷2)(104+105) + (25÷2)(105+109) + (25÷2)(109+120)

= 10575m²

Question 17

a pool is shaped like an irregular quadrilateral, with a curved side. the side parallel to the curved side has a length of 10m, and the other two sides have lengths of 3m and 15m respectively. estimate the volume of the pool if its depth everywhere is 1.8m. answer correct to the nearest cubic metre.

Answer 17

A ≈ w (df + dl)
–
2

= (10÷2)(3+15)
= 90
90 x 1.8
= 162m³