(WORD) PROBLEMS IN ENGLISH
1)
The charges for Helen’s bill-pay phone per month are as follows:
Fixed charge: €10
Call charges:
First 40 minutes: 25 cent per minute - Additional minutes: 15 cent per minute
Text messages: 12 cent each
During March, Helen used 60 minutes call time and sent 30 text messages.
(i) Calculate the total charge for all her phone calls.
(ii) Calculate the charge for her text messages.
(iii) Calculate Helen’s bill, after VAT at 21% is added to all the above charges.
2)
Alan Barry and Colm each bought a ticket for a concert.
Barry paid €5 more than Alan for his ticket.
Colm paid twice as much as Barry.
Alan’s ticket cost € x.
(i) Write an expression in x for the price that Barry paid.
(ii) Write an expression in x for the price that Colm paid.
(iii) Given that the total paid out by the three friends was €95,
how much did Alan pay?
3)
To calculate the time required to roast a chicken the recommendation is:
“45 minutes per kilogram of weight, plus 20 minutes extra”.
When x is the weight in kilograms, this rule can be written as:
Roasting time (in minutes) = 45x +20.
(i) How long will it take to roast a 2·2 kg chicken?
Give your answer in hours and minutes.
(ii) If it takes an hour and twenty minutes to roast a particular chicken, calculate
the weight of the chicken.
4)
A cinema has 500 seats. One night 200 seats were empty.
What percentage of the seats were occupied?
5)
Liam drove from Town A to Town B, a distance of x km.
He then drove from Town B to Town C, a distance of (2x + 1) km.
The total distance that he drove was 56 km.
Find the value of x, correct to the nearest kilometre.
6)
Aoife and John are the same age as each other and Frank is 2 years older than them.
Let Aoife’s age be x years.
(i) Write an expression for Frank’s age in terms of x.
(ii) Write an expression in x for the sum of their three ages.
(iii) In four years time the sum of their ages will be 65. What age is John now?
7)
The value of a computer depreciates at the rate of 20% per year.
At the end of the first year a computer is worth €656.
(i) Find the value of the computer when it was new.
(ii) What will the computer be worth at the end of the third year?
Give your answer to the nearest euro.
8)
An auctioneer sells a house for €830,000. The auctioneer’s fee is 1·5% on
the first €500,000 and 2·5% on the remainder.
Calculate the auctioneer’s fee.
9)
A survey of 40 students was carried out to find how many owned an MP3 player, a
digital camera or a CD player.
1 student does not own any of these.
x students own all three, while 2x own an MP3 player and a digital camera but not a
CD player.
10 own an MP3 player and a CD player, while 11 own a digital camera and a CD
player.
22 own an MP3 player, 22 own a digital camera and 24 own a CD player.
(i) Construct a Venn diagram and solve for x.
(ii) Hence, calculate the percentage of students who own one item only.
10)
Laura, Barry and David use their mobile phones to send text messages.
In one week they sent a total of 74 messages.
Laura sent x messages. B.arry sent twice as many as Laura.David sent 8 messages.
(i) Write the above information as an equation in x.
(ii) Solve the equation to find the value of x.
(iii) How many messages did Barry send?
(iv) Write the number of messages sent by Laura as a percentage of the
total number of messages sent, correct to the nearest whole number.
11)
A shop sells loose sweets by weight. Peter bought 250 grammes of sweets for €1.75.
(i) Ann bought 300 grammes of the sweets. How much did she pay?
(ii) Brian spent €3.15 on sweets. How many grammes did he get