# THE RATIO OF HORSES AND COWS AT THE FARM (CAMBRIDGE PAST PAPER)

A farmer has 45 horses and 20 cows.
(i)  Write this as a ratio horses : cows.
(ii) The farmer wants the ratio horses : cows to equal 5 : 3.
He keeps his 45 horses but buys some more cows. Work out the number of cows he must buy. Mathematics Cambridge IGCSE Test (0580 m16 qp 32)

(i) The ratio is always expressed in the simplest form
45 : 20
Divided by 5 to become
9:4
(ii) In this case, it must be answered by algebraic expression.
Because we have not know how many cows more to be bought yet, so it is expressed by x.
The algebraic expression is become
45: (20+x)=5:3
With cross multiplication
45x3 = 5(20+x)
135 = 100 + 5x
35 = 5x
7 = x
So the number of cows he must buy are 7.

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SIMILAR  QUESTION (EXAMPLE QUESTION ONLY)

One of Texas Attorney has 75 horses and 55 buffaloes.
(i) Write this as a ratio horses : buffaloes.

(ii) The Texas Attorney wants the ratio horses : buffaloes to equal 5 : 4.
He keeps his 75 horses but buys some more buffaloes.
Work out the number of buffaloes Texas Attorney must buy.

(i)The ratio is always expressed in the simplest form
75 : 55
Divided by 5 to become
15:11

(ii)  In this question, have to processed algebraically.
Because Texas Attorney haven’t know how many buffaloes more to be bought yet, so it is
expressed by x.
The algebraic expression is become
75: (55+x)=5:4
With cross multiplication
75x4 = 5(55+x)
300 = 275 + 5x
25 = 5x
5 = x
So the number of buffaloes TexasAttorney must buy are 5 buffaloes.