 # Ratio and Proportion Word Problems

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Examples, solutions, and videos to help GCSE Maths students learn how to solve ratio and proportion word problems.

Proportion (recipes) - Question 1 Edexcel GCSE Maths
Examples:
1. Here are the ingredients to make 8 pancakes
a) Jacob makes 24 pancakes.
Work out how much milk he needs.
b) Cathie makes 12 pancakes
Work out how much flour she needs.
2. Sam wants to make soup for 9 people.
Work out how much of each ingredient he needs.
3. Amelia wants to make soup for 9 people.
Work out how much of each ingredient she needs.
Ratio and proportion
Solving direct and inverse proportion problems
Examples:
1. y is directly proportional to x, where y is 10, x is 2. Find the formula and solve when y is 25.
1. y is inversely proportional to x, where y is 10, x is 2. Find the formula and solve when y is 25.

GCSE Revision - Recipe & Proportion
Examples:
Here are the ingredients needed to bake a cake for 8 people.
1. How much of each ingredient is needed for a cake for 20 people?
2. Colin wants to make a cake for 12 people and has the following ingredient in his cupboard. Does Colin have enough to make a 12 person cake?
3. Here are the ingredients needed to make 16 gingerbread men.
Hamish wants to make 24 gingerbread men.
Work out how much of each ingredient he needs.
4. Here is a list of ingredients for making 12 small cakes.
Joe is going to make 24 of the small cakes.
a) Work out how much margarine he needs.
Sharon is going to make 18 of the small cakes.
a) Work out how much flour she needs.
GCSE Maths Revision - Direct and Inverse proportion
Examples:
1. y is directly proportional to x.
When x = 30, y = 45
Find y when x = 40
2. The voltage, V volts, across an electrical circuit is directly proportional to the current, I amps, flowing through the circuit.
When I = 12, V = 78
a) Express V in terms of I.
b) Find V when I = 2.
c) Find I when V = 162.5
3. The area, A cm2 of a square is proportional to the square of its perimeter, Pcm. When P = 8, A = 4. Find a formula for A in terms of P.
4. y is proportional to the square of x.
y = 60 when x = 6
a) Find a formula for y in terms of x
b) Find y when x = 4.5
a) Find a value of x for which y = 135
5. The mass, M kg, of a solid cube made from lead is proportional to the cube of the length, L am, of an edge. When L = 0.2, M = 90
a) Find a formula for M in terms of L.
b) Find the value of M when L = 0.3
c) Find the value of L when M = 2000.
6. When a fixed volume of water is poured into a cylindrical jar, the depth, D cm, of the water is inversely proportional to the cross-sectional area, A cm2, of the cylindrical jar.
When A = 40, D = 120.
a) Find a formula for A in terms of D
b) Find A when D = 150
c) Find D when A = 60

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