Hey there! Sign in to join this conversationNew here? Join for free
 You are Here: Home >< Maths

# Crazy, logical algebraic GCSE Problem???? Watch

1. Hello, can anybody solve these crazy algebra questions?

1.) The cost of hiring a car is £P plus x pence for each mile driven. Find an algebraic expression for the cost of hiring a car and driving it 500 miles, giving your answer:

a.) In £ b.) In pence

2.) The price of an orange is 15 pence and the price of a lemon is 25 pence. A shopper buys 50 fruit of which x are oranges and the rest are lemons.

a.) Find the number of lemons in terms of x.
b.) Find the cost of the lemons in terms of x.
c.) Find the cost of the oranges in terms of x

The total cost of the 50 fruit is £8.50

-Form an equation involving x
-Solve the equation and hence find the cost of the lemons.
2. (Original post by Little Isis)
Hello, can anybody solve these crazy algebra questions?

1.) The cost of hiring a car is £P plus x pence for each mile driven. Find an algebraic expression for the cost of hiring a car and driving it 500 miles, giving your answer:

a.) In £ b.) In pence

2.) The price of an orange is 15 pence and the price of a lemon is 25 pence. A shopper buys 50 fruit of which x are oranges and the rest are lemons.

a.) Find the number of lemons in terms of x.
b.) Find the cost of the lemons in terms of x.
c.) Find the cost of the oranges in terms of x

The total cost of the 50 fruit is £8.50

-Form an equation involving x
-Solve the equation and hence find the cost of the lemons.
First one:
Let C = Total Cost, then C = . . .
3. (Original post by Little Isis)
Hello, can anybody solve these crazy algebra questions?

1.) The cost of hiring a car is £P plus x pence for each mile driven. Find an algebraic expression for the cost of hiring a car and driving it 500 miles, giving your answer:

a.) In £ b.) In pence

2.) The price of an orange is 15 pence and the price of a lemon is 25 pence. A shopper buys 50 fruit of which x are oranges and the rest are lemons.

a.) Find the number of lemons in terms of x.
b.) Find the cost of the lemons in terms of x.
c.) Find the cost of the oranges in terms of x

The total cost of the 50 fruit is £8.50

-Form an equation involving x
-Solve the equation and hence find the cost of the lemons.
Start a bit at a time. With question 1, how do you think you would start off writing the total cost in either pounds or pence (choose whichever one you feel more comfortable with).

For 2, you need to convert things to algebra and set up some simultaneous equations. Can you have a go at this?
4. (Original post by joostan)
First one:
Let C = Total Cost, then C = . . .
C= P+x(500)

Not sure if this is right, but for a.) and b.) it's asking for an algebraic answer, not an actual numerical one?
5. (Original post by davros)
Start a bit at a time. With question 1, how do you think you would start off writing the total cost in either pounds or pence (choose whichever one you feel more comfortable with).

For 2, you need to convert things to algebra and set up some simultaneous equations. Can you have a go at this?
So there's a numerical answer to this problem?

I still don't quite understand question 2...
6. (Original post by Little Isis)
C= P+x(500)

Not sure if this is right, but for a.) and b.) it's asking for an algebraic answer, not an actual numerical one?
that is an algebraic answer

Is it the answer to (a) or (b)
7. (Original post by TenOfThem)
that is an algebraic answer

Is it the answer to (a) or (b)
I don't know, i was answering the previous poster about the total cost.
8. Apparently these questions are easy. I feel like giving up....
9. (Original post by Little Isis)
I don't know, i was answering the previous poster about the total cost.
If x is in pence, what can you tell me about 500x in pounds?
10. (Original post by Little Isis)
C= P+x(500)

Not sure if this is right, but for a.) and b.) it's asking for an algebraic answer, not an actual numerical one?
That's a start, but remember that P is in pounds and x is in pence.

So, you need 2 versions of this formula: one that converts P into pence so that everything is in pence; and another version where you convert x into pounds so that everything is in pounds
11. (Original post by joostan)
If x is in pence, what can you tell me about 500x in pounds?
Is it x X 500=P??
12. (Original post by davros)
That's a start, but remember that P is in pounds and x is in pence.

So, you need 2 versions of this formula: one that converts P into pence so that everything is in pence; and another version where you convert x into pounds so that everything is in pounds
So would i need to multiply in one equation and divide in the other?
13. (Original post by Little Isis)
So would i need to multiply in one equation and divide in the other?
At the moment you have C = P (pounds) + 500x (pence)

So if P is in pounds, what is P in pence? That gives you one version of the formula you need.

For the other version, keep P in pounds and convert 500x pence into pounds (you might find it easier to think of it as 500 pence times 'x').

14. (Original post by davros)
At the moment you have C = P (pounds) + 500x (pence)

So if P is in pounds, what is P in pence? That gives you one version of the formula you need.

For the other version, keep P in pounds and convert 500x pence into pounds (you might find it easier to think of it as 500 pence times 'x').

Sorry i give up on these questions, i find algebra to be quite tricky

Thanks for your help and everyone else's
15. Wait, i don't think i even read the question properly. If x is pence and i drive 500 miles thats 500p and 500p= £5??
16. (Original post by Little Isis)
Wait, i don't think i even read the question properly. If x is pence and i drive 500 miles thats 500p and 500p= £5??
Yep so £5x is the 500x sorted
17. (Original post by joostan)
Yep so £5x is the 500x sorted
Wait so £5x is £P?

Sorry if all my answers and questions sound stupid, i've been i'll all weekend with migraines and what not
18. (Original post by Little Isis)
Wait so £5x is £P?

Sorry if all my answers and questions sound stupid, i've been i'll all weekend with migraines and what not
No . . .
Spoiler:
Show
C= P +5x (in pounds)
19. (Original post by Little Isis)
Wait, i don't think i even read the question properly. If x is pence and i drive 500 miles thats 500p and 500p= £5??
Ok

So think about a numerical question

Cost = £4 plus 3p a mile and I go 500 miles

So remember that in £ I start with £4 but in pence I will start with 400p

I will find the milage part by doing 3 x 500 = 1500p or 3 x 5 = £15

So my cost is
£
4 + 15 = £19

or pence
400 + 1500 = 1900p

Both the red parts involved multiplying by 3 so if the cost is x pence for each mile they will be multiplied by x instead

So instead of 3x5 = 15 we just have 5x
Or instead of 3x500 = 1500 we just have 500x

So the costs would be

£
4 + 5x

pence
400 + 500x
20. (Original post by TenOfThem)
Ok

So think about a numerical question

Cost = £4 plus 3p a mile and I go 500 miles

So remember that in £ I start with £4 but in pence I will start with 400p

I will find the milage part by doing 3 x 500 = 1500p or 3 x 5 = £15

So my cost is
£
4 + 15 = £19

or pence
400 + 1500 = 1900p

Both the red parts involved multiplying by 3 so if the cost is x pence for each mile they will be multiplied by x instead

So instead of 3x5 = 15 we just have 5x
Or instead of 3x500 = 1500 we just have 500x

So the costs would be

£
4 + 5x

pence
400 + 500x
Ahhh, much more understandable. so the answer should be in pounds £P+5x and in pence P+500x?

Reply
Submit reply
TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Updated: May 12, 2013
Today on TSR

### Am I pregnant?

...or just paranoid?

### A robot wrote Harry Potter?

Discussions on TSR

• Latest
• ## See more of what you like on The Student Room

You can personalise what you see on TSR. Tell us a little about yourself to get started.

• Poll
Useful resources

## Make your revision easier

### Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

### How to use LaTex

Writing equations the easy way

### Study habits of A* students

Top tips from students who have already aced their exams

Can you help? Study help unanswered threads

## Groups associated with this forum:

View associated groups
Discussions on TSR

• Latest
• ## See more of what you like on The Student Room

You can personalise what you see on TSR. Tell us a little about yourself to get started.

• The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.