SOLUTION: A boy bought 2 oranges, 3 pears and 4 apples, for 22 cents. He gave as much for a pear as for 2 apples; and twice as much for an orange, as for a pear and an Apple. What was the pr

Algebra ->  Equations -> SOLUTION: A boy bought 2 oranges, 3 pears and 4 apples, for 22 cents. He gave as much for a pear as for 2 apples; and twice as much for an orange, as for a pear and an Apple. What was the pr      Log On


   

Question 1078972: A boy bought 2 oranges, 3 pears and 4 apples, for 22 cents. He gave as much for a pear as for 2 apples; and twice as much for an orange, as for a pear and an Apple. What was the price of each?
Found 2 solutions by josgarithmetic, josmiceli:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
apple, 1 cent each
orange, 6 cent each
pear, 2 cent each

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = the price in cents of an orange
Let +b+ = the price in cents of a pear
Let +c+ = the price in cents of an apple
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(1) +2a+%2B+3b+%2B+4c+=+22+
(2) +b+=+2c+
(3) +a+=+2%2A%28+b+%2B+c+%29+
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There are 3 unknowns, so 3 equations are given
Substitute (2) into (3)
(3) +a+=+2%2A%28+2c+%2B+c+%29+
(3) +a+=+2%2A3c+
(3) +a+=+6c+
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Substitute (2) and (3) into (1)
(1) +2%2A6c+%2B+3%2A2c+%2B+4c+=+22+
(1) +12c+%2B+6c+%2B+4c+=+22+
(1) +22c+=+22+
(1) +c+=+1+
and
(2) +b+=+2c+
(2) +b+=+2%2A1+
(2) +b+=+2+
and
(3) +a+=+6c+
(3) +a+=+6%2A1+
(3) +a+=+6+
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The price of an orange is 6 cents
The price of a pear is 2 cents
The price of an apple is 1 cent
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check answers:
(1) +2a+%2B+3b+%2B+4c+=+22+
(1) +2%2A6+%2B+3%2A2+%2B+4%2A1+=+22+
(1) +12+%2B+6+%2B+4+=+22+
(1) +22+=+22+
You can check (2) and (3)