1. Applied Arithmetic – Learning Outcomes
Solve problems about transactions, including
VAT
currency exchange
bills
meter readings

2. Solve Problems about VAT
VAT comes in five rates:
Standard rate (23%) – most goods and services.
Reduced rate (13.5%) – certain fuels, building services, cleaning and maintenance services, photographic supplies.
Second reduced rate (9%) – various tourism-related goods and services (e.g. restaurants, shows, museums).
Livestock rate (4.8%) – livestock used in food preparation.
Flat-rate compensation percentage for farmers (5.2%) – applies to certain farmers.

3. Solve Problems about VAT
Percentages are ratios compared to 100 (per cent – per hundred).
e.g. 20% means 20:100 or
Lara buys a radio. The original price of the radio before tax was € If the VAT rate is 23%, what did Lara pay for the radio?
Seán pays for a meal in a restaurant. The bill comes to €43.20 after tax. Assuming Seán paid 9% tax, what was the price of the meal before tax?

4. Solve Problems about VAT
2004 OL P1 Q3
VAT at 15% is added to a bill of € Calculate the total bill.
2006 OL P1 Q3
VAT at 21% is added to a bill of €750. Calculate the total bill.
2007 OL P1 Q3
VAT at 21% is added to a bill of €255. Calculate the total bill.
2008 OL P1 Q3
VAT at 13.5% is added to a bill of €860. Calculate the total bill.
2011 OL P1 Q3
A washing machine costs €320 plus VAT at 21.0%. Calculate the total cost of the washing machine after VAT is added.

5. Solve Problems about VAT
2014 OL P1 Q7
VAT in Ireland is charged at different rates on different items. For instance:
Children’s shoes have a VAT rate of 0%.
Bulls have a VAT rate of 4.8%.
Newspapers have a VAT rate of 9%.
A pair of children’s shoes cost €20 before VAT is added. Write down the cost of the shoes after VAT is added.
A bull is sold for €1600 before VAT is added. Find the cost of the bull after VAT is added.
A newspaper costs €2.18 after VAT is added. Find the cost of the newspaper before VAT is added.

6. Solve Problems about Currency Exchange
The value of currencies is usually given as a ratio.
e.g. €1:$1.12 means €1 can be exchanged for $1.12.
e.g. €1:£0.87 means €1 can be exchanged for $0.87.
Cian is travelling to London at the weekend and wants to change €200 into pounds. How many pounds will he get if the exchange rate is €1:£0.87?
Charles is returning home from a holiday to America and wants to change her remaining $140 back to euro. If the exchange rate is €1:$1.12, how many euro will he get back?

7. Solve Problems about Currency Exchange
2003 OL P1 Q2
1 euro = 120 Japanese yen. Change 3000 yen to euro.
2006 OL P1 Q2
On a day when €1 = $1.21, find the value in euro of $6655.
2008 OL P1 Q2
On a day when €1 = £0.68, find the value in euro of £816.
2011 OL P1 Q2
Before going on holidays to the USA, Seán changed €500 into dollars. The exchange rate was €1 = $1.22.
How many dollars did Seán get?
When Seán came home he changed $50 back into euro. The exchange rate was the same.
How much, in euro, did Seán receive? Give your answer to the nearest cent.

8. Solve Problems about Bills
Bills can come with a variety of charges.
Standing charge – rate per day for using the service.
Charge per unit – rate per unit of service (gas, electricity minutes etc.) used.
Taxes.

10. Solve Problems about Bills
Becky has Meteor’s “lite” plan, and used 560 MB of data and 130 minutes last month. What is her total bill?

11. Solve Problems about Bills
If you use 5000 kWh in a year, which of the following two electricity suppliers would be cheaper?

12. Solve Problems about Bills
2006 OL P1 Q3
Find the total cost of the following bill:
6 litres of milk at €1.05 a litre,
3 loaves of bread at €1.20 a loaf,
5 apples at 65c each.
2007 OL P1 Q3
In one week Bríd sent 26 text messages on her phone.
11 of these messages cost 8c each.
The rest of the messages cost 12c each.
Find the total cost of Bríd’s texting that week.

13. Solve Problems about Bills
2005 HL P1 Q2
The monthly line rental on Peter’s mobile phone amounts to € During May, the duration of his calls is 1 hr 41 mins and 50 s. Calls are charged at 0.6c per second.
Calculate Peter’s total bill for May.
2012 OL P1 Q2
Cathy wants to pay her electricity bill. Electricity costs 20c per unit. She has used 250 units. The bill also has a standing charge of €30.
Calculate the electricity bill.

14. Solve Problems about Bills
2012(S) FL P1 Q7
An extract from an electricity bill is shown. Some of the numbers are labelled A, B, C, D, E, F. Calculate the missing numbers.

15. Solve Problems about Bills
2016 OL P2 Q8
John compiled a table showing the amount of water used in his own household over the course of a week. He recorded the number of litres required for each activity and the number of times each activity was undertaken. The data are shown in the table below.
Complete the table to show the number of litres used for the various activities and the total number of litres used in the week.
If water were charged at €1.85 per 1000 litres, find what John’s household would pay for the water used in one year if the household uses the same amount of water each week.

16. Solve Problems about Bills

17. Solve Problems about Bills
Find John’s total bill for this water if VAT were to be included at a rate of 13·5%.
John would like to reduce his water bill to €260 per year. If water were charged at €1·85 plus VAT at 13·5% per litres, find the number of litres of water he could purchase for €260.