Sec. 4 Direct and Inverse Proportion Flashcards
Hannah pays £3.60 per 400g of cheese. She uses 220g of cheese to make 4 cheese pastries.
How much would the cheese cost if she had to make 50 cheese pastries?
In 1 pastries there is: 220g÷4=55g of cheese
So in 50 pastries there is: 55gx50=2750g of cheese
1g of cheese would cost: £3.60÷400=0.9p
So 2750g of cheese would cost: 0.9x2750=2475p= £24.75
a) What is direct proportion?
b) What is inverse proportion?
a) If quantity A increases, quantity B will increase relative to the amount of quantity A.
b) Where one quantity A, increases, another quantity B decreases relative to the amount.
4 bakers can decorate 100 cakes in 5 hours.
a) How long would it take 10 bakers to decorate the same number of cakes?
b) How long would it take11 bakers to decorate 220 cakes?
a) 100 cakes will take one baker: 5x4=20 20 hours
So 100 cakes will take 10 bakers: 20/10= 2 hours for 10 bakers.
b) 100 cakes will take 1 baker: 20 hours
1 cake will take 1 baker: 20÷100=0.2 hours
220 cakes will take 1 baker: 0.2x220=44hrs
220 cakes will take 11 bakers: 44÷11=4 hours
a) How can you write ‘y is proportional to x’ and ‘y is inversely proportional to to x’ as an equation (an equation with ‘k’)?
b) How can you write the following as equations (and as equations with k):
i) ‘y is proportional to the square of x’
ii) ‘t is proportional to the square root of h’
iii) ‘v is inveresly proportional to r cubed’
a) y is proportional to x: y ∝ x ( y=kx)
y is inverely proportional to x: y ∝ 1/x (y=k/x)
b)
i) y ∝ x2 y=kx
ii) t ∝ √h t=k√h
iii) v ∝ 1/r3 v=k/r3
What are the graphs for:
- y is propotional to x
- y is inversely proportional to x
- y is proportional to x2
- y is inversely proportional to x3
b) e.g. G is inversely proportional to the square root of H. When G=2 H=16.
Find an equation for G in terms of H, and us eit to work out the value of G when H=36.
a) How do you handle algebra in proportion:
