Question 206742: John and Charles buy red and blue certificates. John buys 10 red and 20 blue and pays $40. Charles buys 10 blue and 20 red and pays $50. The following day, they find out that they need more certificates and they go together to buy 3 red and 2 blue. How much did they pay for these five certificates?
(A) $5 (B) $6 (C) $7 (D) $8 (E) $9
Answer by profemmanuel2q@yahoo.com(15)   (Show Source):
You can put this solution on YOUR website!
Before you solve this, you have to know the price for one blue and red certificate.
Let red and blue certificate be x and y respectively.
John buys 10 red and 20 blue and pays $40. This can be expressed as 10x + 20y = 40
Charles buys 10 blue and 20 red and pays $50. this is also 20x + 10y = 50
10x + 20y = 40 ------- Eqn 1
20x + 10y = 50 ------- Eqn 2
Multiply Eqn 1 by 2
20x + 40y = 80 ------- Eqn 1
20x + 10y = 50 ------- Eqn 2
Eqn. 1 - Eqn. 2
30y = 30
Divide both side by 30
y = 1
Put y = 1 into eqn. 1
10x + 20(1)= 40
10x + 20 = 40
10x = 40 - 20
10x = 20
Divide both side by 10
So we have x = 2
Hence, x = 2 and y = 1
So one red certificate cost $ 2 and one blue certificate cost $ 1
So the cost for 3 red certificates is 2 x 3 = $ 6
And the cost of 2 red certificates is 1 x 2 = $ 2
Total will be $ 6 + $ 2 = $ 8
Hence, they pay $ 8 for these five certificates.
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