maths problem given to a 10 year old?

Question

4 footballs and 3 tennis balls cost £15.60
3 footballs and 4 tennis balls cost £15.20
how much does one football cost?
how much does one tennis ball cost?

Answer 1

USING SIMULTANEOUS EQUATIONS:

4F + 3T = 15.60
3F + 4T = 15.20

Multiply the first by 3:
12F + 9T = 46.80

Multiply the second by 4:
12F + 16T = 60.80

Subtract the second from the first:
7T = 14
T = 2

Putting that back into the original equation:
4F + 3(2) = 15.60
4F = 15.60 - 6
4F = 9.60
F = 2.40

So the answers are:
Football = £2.40
Tennis ball = £2.00

Double check:
4(2.40) + 3(2) =?
9.60 + 6 = 15.60 <-- correct

3(2.40) + 4(2) =?
7.20 + 8 = 15.20 <-- correct

So this is the correct answer:
Football = £2.40
Tennis ball = £2.00

POSSIBLY EASIER WAY TO LOOK AT THIS:

Perhaps a simpler way to look at this is:
4 footballs and 3 tennis balls = £15.60

If you replace one of the footballs with a tennis ball (3 footballs and 4 tennis balls), the price goes down by £0.40. That tells us that a tennis ball costs £0.40 less than a football.

So if we were to replace all the footballs with tennis balls (0 footballs and 7 tennis balls), we would expect it to go down 4 x £0.40 or £1.60.

So 7 tennis balls = £15.60 - £1.60 = £14.00.

It's simple division and addition to see that each tennis ball is £2.00 and each football is £2.40.

Answer 2

VantheMan has the correct solution although I fail to see why he needed to end up with two ( - ) terms.

This is definitely NOT a problem that a 10 year old should be asked to solve unless, of course, he happens to be a child mathematical prodigy.

Incidentally, I would have preferred those using a simultaneous equation method to use the terms F for football and T for tennis as the unknown quantities.

This would automatically indicate the cost of a Football and that of a Tennis ball.

X and Y are the generic terms for the axes of a Graphical solution but in any such context the axes would be LABELLED as Footballs and Tennis balls. The terms X and Y do not appear in the original question.

Answer 3

I don't know if a 10 yr old would be expected to work this out formally, as simultaneous equations.

So I did it by common sense.
1 foot ball costs 15.60 less the cost of 3 footballs and 3 tennis balls
1 tennis ball costs 15.20 less the cost of 3 footballs and 3 tennis balls
So a football costs 40p more than a tennis ball.
So 4 foot balls and 3 tennis balls would cost 1.60 more than 7 tennis balls
so 7 tennis balls cost £14
1 tennis ball costs £2
1 football costs £2.40

It is the first step that is hard, spotting that a foot ball costs 40p more than a tennis ball. There are several ways to do it. As usual with maths problems. The main thing is not to be scared of the problem and to try out different things.

It works by checking.

Answer 4

Football = £2.40
Tennis ball = £2

Seems like a tricky problem for a ten year old!

EDIT
Although the posts that answer the question using simultaneous equations are correct, it is unlikely that this is the approach the teacher wanted given that the child is 10 years old. I suspect she's looking for something like the answer that tigger posted below:

Answer 5

It seems like most people have the right methods, but have failed to perform the math correctly. We start with:

3 footballs and 4 tennis balls cost £15.20
4 footballs and 3 tennis balls cost £15.60

...or...

3 f + 4 t = 15.2
4 f + 3 t = 15.6

...multiplying the first by 4 and the second by 3...

12 f + 16 t = 60.8
12 f + 9 t = 46.8

...subtracting the second from the first...

7 t = 14 or t = 2

...so there you have it. A tennis ball is 2 pounds. To figure out the football, substitute:

4 f + 3 t = 15.60

...giving...

4 f + 6 = 15.60

...subtracting...

4 f = 9.6 or f = 2.4

...So a tennis ball is 2 pounds and a football is 2.4 pounds.

Hope that helps!

Answer 6

If I've worked this out correctly then tennis balls are all £2 and footballs are £2.40.

This is because 4F + 3T =£15.60
But at the same time 3F + 4T = £15.20.
This gives you two equations in F and T whichare completely solvable. By working out what one football costs, by doing:
3F/3 + 4T/3 = £15.20/3
and rearranging:
F = £15.20/3 - 4T/3
you can then multiply this by four to get what 4F equals, and then you can stick this in the first equation. The numbers may look a bit odd at first, but it will give you an equation in T, which will enable you to find out that T is £2. After that you just stick £2 in instead of T in one of the original equations to find out what F equals.

Answer 7

Solve using simultaneous equations.

Football = £2.40
Tennis Ball = £2

Answer 8

There is nothing here that a ten year old shouldn't be able to deal with. It's only simple addition and subtraction you're dealing with. I was doing long division when I was 7.

Answer 9

haha,, giving to a ten year old ??? any 10 year old who can tell this, i would like to meet :)

what i also find funny is that everyone here has giving a wrong answer here(at time of post) :((
ill spell it out to you like u where a 10 year old though :)
we have 4F + 3T = 15.60 <-- times by 3
3F + 4T = 15.20 <-- times by 4

12F + 9T = 46.80
12F + 16T = 60.80

Now we can see that,,,, 16T - 9T = 60.80 - 46.80
7T = 14
T = 14/7 =2

3F + 4(2) = 15.30
3F = 15.20 - 8
3F = 7.2
F = 2.40

so,,,, tennis balls cost 2 pounds
footballs cost 2.40 pounds

shocking really ....

Answer 10

Footballs are 40p pence dearer than tennis balls
(we know this because 4 footballs and 3 tennis balls cost forty pence more than 3 footballs and 4 tennisballs)

so if we take 4*0.40 of all the balls would cost the same price.

15.60 - 1.60 = 14.00

14 divided by 7(the total number of tiems borought) is 2

a football is therefor 2.40
a tennis ball is 2

check it (4*2.40) 9.60 + (3*2) 6 = 15.60
(3*2.40) 7.20 + (4*2) 8 = 15.20