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Question 1079216: David counted the birds in his garden, One third of the birds were cockatoos and one quarter were pigeons. He saw six more cockatoos than pigeons. How many birds did David see?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! let x = the number of birds in the garden.
number of cockatoos = 1/3 * x
number of pigeons = 1/4 * x.
number of cockatoos = 6 more than number of pigeons.
let c = number of cockatoos.
let p = number of pigeons.
you get:
c = 1/3 * x
p = 1/4 * x
c = p + 6
replace c with p + 6 in the first equation and the first and second equations become:
p + 6 = 1/3 * x
p = 1/4 * x
subtract 6 from both sides of the first equation and both equations become:
p = 1/3 * x - 6
p = 1/4 * x
since p = p, then 1/3 * x - 6 must be equal to 1/4 * x
you get:
1/3 * x - 6 = 1/4 * x
subtract 1/4 * x from both sides of this equation and add 6 to both sides of this equation to get:
1/3 * x - 1/4 * x = 6
multiply both sides of this equation by 12 to get:
4 * x - 3 * x = 72
combine like terms to get:
x = 72.
that's the number of birds that dave saw.
number of cockatoos = 1/3 * 72 = 24
number of pigeons = 1/4 * 72 = 18
number of cockatoos minus number of pigeons = 6.
solution looks good.
the whole idea is to reduce the number of unknown variables so that they are equal to the number of equations.
this allows you to solve for the variables.
your variables were c and p.
by replacing c with its equivalent value of p + 6, you were able to reduce the number of unknown variables from 3 to 2.
you wound up with a system of 2 equations in 2 unknown variable which was then able to be solved.
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