Question 12229: A person has a basket of fruit, consisting of apples, oranges and bananas. The total pieces of fruit is equal to 80. The number of oranges is 5 more than 1/3 of the number of apples. The number of bananas is 1 less than 1/4 the number of apples. How many of each fruit will you have?
Answer by kusha(21)   (Show Source):
You can put this solution on YOUR website! Let the no. of apples be x, the number of bananas be y and the number of oranges be z.
then x+y+z = 80 (given total of all these fruits)
Z = (1/3)x + 5 given in question that oranges are 5 more than one-third of apples
y = (1/4)x - 1 given in question
Now we have three equations and consider the ques solved cause in simple equations we can solve as many varibles as are the number of equations e.g.
here let us substitute the vlue of x & y in original equation.
x + (1/4)x + 5 + (1/3)x - 1 = 80
(19/12)x + 4 = 80
(19/12)x =80-4
x = 76 x (12/19)
x = 48 thus no. of apples is 48
z = (1/3)x + 5 from earliar eqn. thus z =21 hence oranges are 21
and balance 80 - (48 + 21) = 11 would be bananas
alternatively we can also find bananas by substituting value of x in the eqn
y = (1/4)x - 1
So apples = 48, bananas = 11, oranges = 21
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