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Mixed ratio problems
Direct proportion
Problems with k
Divide a quantity in a given ratio
Inverse variation
100
A motorbike uses petrol and oil mixed in the ratio 13 : 2. How much of each is there in a 90 litres of mixture?
78 l petrol and 12 l oil
100
A recipe needs 400g of flour to make 8 cakes. How much flour would be needed in order to make two dozen cakes?
1200g
100
Mr. Calin' Maths class decided to do a car-wash fundraiser to support the Holidays. If we could write a formula to predict our success, it would equate to the number of Students (S) involved varies directly with the number of cars (C) that are washed, but varies indirectly with the amount of time (T) it takes to wash any number of cars. Translate this word problem into a variation formula.
S = k x C / T
100
A ruler 30 cm long is broken into two parts in the ratio 8:7. How long are the two parts?
16 cm and 14 cm
100
A school can buy 200 textbooks with $18 each. If the price is cut in half, how many can they buy with the same amount?
400 textbooks
200
A piece of wood is cut in the ratio 3 : 7. If the wood is 1.5 m long, how long is the shorter piece (in cm)?
45 cm
200
To make 6 jam tarts, 120 g of jam is needed. How much jam is needed to make 10 tarts?
200g
200
Time (T) it takes to make 100 BMWs varies indirectly with the number of machines (M) that function on its assembly line. If in 6 hours, with 7 machines, they make 100 cars, find the constant of variation and find the number of machines that have to function to make 10 cars in 21 hours.
k = 42, M = 2
200
Divide 30 minutes in the ratio 2:3.
12 to 18
200
Six people can paint a room in 8 hours. How long would it take 9 people? (in hours and minutes)
5 h 20 minutes
300
Divide 3 tonnes in the ratio 2 : 5 : 13. Epress answers in kg.
300 : 750 : 1950
300
A recipe for two people requires 1/4 kg of rice to 150 g of meat. How much meat would be needed for five people?
375 g
300
The curve (C) of a pitch varies jointly with the amount of force (f) that is thrown and the rotation (r), but varies inversely against the wind speed (w). If (k) is the constant of proportionality for this relationship, write the formula. If C = 30, f = 10, r = 6 and w = 8, find the constant of proportionality.
C=(k x f x r)/w; k = 4
300
The angles of a triangle are in the ratio 2 : 5 : 8. Find the size of each of the angles.
24, 60, 96 degrees
300
It takes 16 hours for three bricklayers to build a wall. Calculate how long it would take for eight bricklayers to build a similar wall?
6 h
400
A large swimming pool takes 36 hours to fill using three identical pumps. How long would it take to fill using 8 identical pumps?
13.5 h
400
The scale of a map is 1 : 25 000. Two villages are 8 cm apart on the map. How far apart are they in real life? Give your answer in kilometres.
2 km
400
The number of Students (S) involved varies directly with the number of cars (C) that are washed, but varies indirectly with the amount of time (T) it takes to wash any number of cars. Translate this word problem into a variation formula. If it takes 5 students 2 hours to wash 16 cars, estimate how many cars can 9 students wash in 1 hour?
14 complete cars
400
An aunt gives a brother and sister $6000 to be divided in the ratio of their ages. If the girl is 13 years old and the boy 12 years old, how much will each get?
Girl $3120, boy $2880
400
A photocopying machine is capable of making 50 copies each minute. If four identical copiers are used simultaneously how long would it take to make a total of 50 copies? (in seconds)
15 s
500
A large swimming pool takes 36 hours to fill using three identical pumps. If the pool needs to be filled in 9 hours, how many pumps will be needed?
12 pumps
500
The scale of a map is 1 : 25 000. The distance from a village to the edge of a lake is 12 km in real life. How far apart would they be in the map? Give your answer in centimetres.
48 cm
500
The number of Students (S) involved varies directly with the number of cars (C) that are washed, but varies indirectly with the amount of time (T) it takes to wash any number of cars. Translate this word problem into a variation formula. The car wash lasted for 3 hours and with 12 students working they were able to wash approximately 200 cars. About how long did it take one person to wash one car?
about 11 min (10.8 min)
500
The ratio of the angles of a quadrilateral is 2:3:3:4. Calculate the size of the smallest angle.
60 degrees
500
A photocopying machine is capable of making 50 copies each minute. How many copiers would be needed to make 6000 copies in 15 minutes?
8 copiers