Number, percentages, and percentiles

Mathematics Worked Examples by Topics

Number	Mathematical Skills	Applications
1	Number, percentages, and percentiles	Determining the amounts, costs, and dimensions of materials
2	Ratio	Scaling models, dimensions, shapes, and drawings
3	Surface area/Volume	Finding costs of quantities, waste amounts
4	Trigonometry	Calculating angles/lengths of products
5	Graphs and charts	Using data to make decisions/visualization of data
6	Coordinates and geometry	Using coordinates for design drawings
7	Statistics	Using data to make informed design decisions

Number, percentages, and percentiles

Question 1)

A cement manufacturer is to provide concrete for a new high speed railway within the UK.

A construction company requires 500 bags of cement a day for construction
The cement manufacturer can create 200 tonnes of cement a day
1 bag of cement weighs 450kg

Calculate whether the cement manufacturer can meet the construction companies cement demand.

Step 1) Calculate the construction companies demand in kg per day:

Demand = 500 x 450 = 225,000kg

Step 2) Convert demand in kg to tonnes:

Demand in tonnes = ^225,000⁄_1,000 = 225 tonnes

Step 3):

As demand is greater than supply the manufacturer cannot meed the demand of the construction company

Question 2)

A new high speed railway will decrease the time taken to travel between London and York by 15 minutes. The journey takes 2.05 hours currently. Calculate the percentage reduction in travel time.

Step 1) Calculate the current journey time in minutes:

Time (minutes) = 2.05 x 60 = 123 minutes

Step 2) Calculate the new journey time:

New time = 123 - 15 = 108 minutes

Step 3) Calculate the percentage reduction in journey time:

Percentage reduction = ^{Old - New}⁄_Old = ¹⁵⁄₁₂₃ = 0.122 = 12.2%

Question 3)

The budget os this high speed railway was estimated to cost £50 million, however, due to rising costs the company responsible estimate the cost will increase by 57%. Work out the new cost of the railway project.

Step 1) Convert the percentage increase into a decimal:

57% = 0.57

Step 2) Calculate the new cost of the project:

New time = 50 x (1 + 0.57) = £78.5 million

Topic test:

Number, Percentages, and Percentiles Questions