Map Scales (1:n & Distances)
A map has a scale of 1 cm : 500 m. Express this scale in the standard ratio format of 1 : n
1 : 50,000(Since 500 m = 50,000 cm).
If the linear map scale of a drawing is 1 : 5, what is its corresponding area scale?
1 : 25 (Since 12: 52 = 1 : 25).
A bakery sells 3 loaves of bread for $4.50. How much will it cost to buy 12 loaves of bread?
$18
A tech store sells 10 tablets and brings in a profit of $500. If their sales drop slightly and they sell only 8 tablets, what will their profit be?
$400
Expand and simplify the expression: 4(x + 5) + 7
4x + 27
A map scale is written as 2 cm : 5 km. If the distance between two villages on the map is 6 cm, what is the actual distance between them in kilometers?
15 km
The area scale of a model park is 1:100. If the area of a playground on the map is 5 cm2, what is the actual area of the playground in cm2?
500 cm2
An athlete runs 60 meters in 12 seconds. At this exact same speed, how long will it take them to run 300 meters?
60 seconds (or 1 minute)
If 3 painters can paint a classroom wall in 8 hours, how many hours would it take 6 painters to paint the exact same wall working at the same pace?
4 hours
Expand and simplify the expression: 3(x + 2) + 5(x + 4)
8x + 26
The scale of a blueprint is 4 mm : 2 m. If the actual length of a hallway is 10 meters, how long will it be on the blueprint in millimeters?
20 mm
A model has a linear scale of 1:20. If the actual floor area of a room is 16,000 cm2, what is the area of the room's floor on the model?
40 cm (Area scale is 1:400, and 16,000 \ 400 = 40$).
A motorbike uses 2 liters of fuel to travel 90 kilometers. How many kilometers can it travel if its tank has 7 liters of fuel?
315 km
A road trip takes 4 hours when a bus travels at an average speed of 60 km/h. How long would the same trip take if the bus traveled at an average speed of 80 km/h?
3 hours
Fully factorize the expressions: (1) 4x2 + 12x and (2) x2 - 49$.
(1) 4x(x + 3) and (2) (x + 7)(x - 7)
A map scale is 1 : 200,000. If a road measures 15 cm on the map, what is the actual length of the road in kilometers?
30 km (15 cm × 200,000 = 3,000,000 cm = 30 km).
A map has an area scale of 1:900. What is the linear scale (1:n) of this map?
1:30
A company determines that it needs 2 supervisors for every 25 factory workers. If the factory hires 175 workers, how many supervisors are required?
14 supervisors
A rectangular water tank with a base area of 6 m2 is filled with water to a depth of 40 cm. If this exact volume of water is poured into a different tank with a base area of 8 m2, what will the new depth of the water be?
30 cm (Total volume = 6 \times 40 = 240; New depth = 240 \div 8 = 30)
A map uses a scale of 15 mm : 600 m. If the actual distance between two docks is 2.4 kilometers, what is their distance on the map in centimeters?
6 cm (2.4 km = 2,400 m. Since 15 mm represents 600 m, the map distance is 60 mm, which equals 6 cm).
The linear scale of a structural map is 1 cm: 4 m. If a lake covers an actual area of $128 m2, what is the area of the lake on the map in cm2?
8 cm2
A printing shop features 8 identical machines that can produce a combined total of 160 banners in 4 hours. If 3 machines break down, how many banners can the remaining working machines produce in that same 4-hour window?
100 banners? (5 working machines × 20 banners per machine).
A construction crew of 15 workers has enough food rations to last for 12 days. If 5 additional workers join the crew on day one, how many days will the food rations last?
9 days? (15 \times 12 = 180 total rations; 180 \div 20 workers = 9).
Expand and simplify the double brackets:(x + 3)(x + 4)
x2 + 7x + 12