1. ## Maths sum

Sally bought some chicken wings and fishballs for a party. The cost of the chicken wings is 4/5 of the money she spent. The cost of each chicken wing to the cost of each fishball is in the ratio of 5:2. Find the ratio of the number of chicken wings to the number of fishballs Sally bought for the party.

PS my friend and I arent 13 yet I'm sorry if its too easy

Anna

2. Hi anna

Let:
number of chicken wings bought = x
number of fishballs bought = y
total money = m
chicken wing = cw
fishball = fb

Originally Posted by AnnaRydell
Originally Posted by AnnaRydell
The cost of the chicken wings is 4/5 of the money she spent.

This means that : x (cw) = 4/5 m

The cost of each chicken wing to the cost of each fishball is in the ratio of 5:2.
This means that : 1 (cw) : 1 (fb) = 5 : 2 or
$\displaystyle \frac{cw}{fb} = \frac {5}{2}$

Find the ratio of the number of chicken wings to the number of fishballs Sally bought for the party.

The question is x : y = ?

Let's start
x (cw) = 4/5 m ------> equation 1
So the cost of the fishballs is 1/5 of the money. This means y (fb) = 1/5 m -------> equation 2

Equation 1 divided by equation 2 will give you result :
$\displaystyle \frac{x (cw)}{y (fb)} = \frac{4/5 m}{1/5 m}$

$\displaystyle \frac{x}{y} = \frac{4 fb}{ cw}$ -----> equation 3

From the question :
$\displaystyle \frac{cw}{fb} = \frac {5}{2}$

$\displaystyle cw = \frac{5}{2} fb$ ----> equation 4

Subs. equation 4 to equation 3 will give you the answer ^^

EDIT : Thx krahl ^^

3. let x be # of chicken wings and y be # of fishballs

cw is the cost of 1 chicken wing and fb is the cost of 1 fishball

m is the amount she spent.

then
$\displaystyle x(cw)=\frac{4m}{5}$ so $\displaystyle x=\frac{4m}{5(cw)}$
$\displaystyle y(fb)=\frac{m}{5}$ so $\displaystyle y=\frac{m}{5(fb)}$

but since the cost ratio is 5:2 so i.e. £5 to £2

$\displaystyle 2(cw)=5(fb)$ then $\displaystyle fb=\frac{2(cw)}{5}$

so

$\displaystyle \frac{x}{y}=\frac{\frac{4m}{5(cw)}}{\frac{m}{5(fb) }}$

$\displaystyle \frac{x}{y}=\frac{4(fb)}{cw}$

substituting $\displaystyle fb=\frac{2(cw)}{5}$

$\displaystyle \frac{x}{y}=\frac{8}{5}$

8:5

Don't worry about asking questions which you think are too easy, this is a place where you are allowed to ask any type of question no matter how easy or hard you may think it to be.

Songoku you may have made a mistake on equation 3 from the previous one.

It should be $\displaystyle \frac{x}{y}=\frac{4fb}{cw}$

4. Thanks a lot, but is it possible to do it in a simpler way? I don't really understand that method, and we seldom use algebra in school to solve questions like that.

Anna

5. The simplest way i can think of anna is that i just decide that i have £100
each chicken wing costs £5 and fishball costs £2.

i find 4/5 of 100 wich is £80 and the remaining is £20

so i know i spent £80 on cw and £20 on fb. Now lets see how many £5's goes into £80. Its 16. And 10 £2's go into £20. So i know i bought 16cw's and 10fb's

so 16:10 and rescaling, 8:5.

Instead of starting it with £100 you could of started it with any amount you choose, its just that 100 seems like a nice round number and divisible by 5 so that's why i chose it.

Do you understand it that way?

(Note:I could even start with £1. but can you see what happens in this case? whenever you get a question like this all you really need to do is
$\displaystyle \frac{\frac{4}{5}}{5}:\frac{\frac{1}{5}}{2}$)

6. I get it now , thanks so much Krahl...!

Anna