Bernard only had durians. Timothy only had apples. They gave each other, half of their fruits. Bernard sold 8 durians and Timothy sold 40 apples. In the end, the ratio of durians to apples for Bernard and Timothy is 1:7 and 1:6 respectively. How many durians did Bernard have at first?
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Expert's answer
2013-07-01T10:22:21-0400
Ifthe amount of durians is x, then the amount of apples will be y. If Bernard and Timothy give each other half of their fruits, it will be x/2 and y/2. If Bernard sold 8 durians and Timothy sold 40 apples, it will be x/2 - 8 and y/2 - 40. If the ratio of durians to apples for Bernard and Timothy is 1:7 and 1:6 respectively, we can construct the following system of equations. (x/2 - 8)/(y/2) = 1 / 7 ; (x/2) / (y/2 - 40) = 1 / 6. Solution: 7*(x / 2 - 8) = 1 * (y/2); 6 * (x/2)= 1 * (y/2 - 40).
7x / 2 - 56 = y / 2; 3 x = (y/2 - 40).
if y/2 = 7x / 2 - 56 Now substitute this expression for y/2 into the other equation
3 x = 7x / 2 - 56 - 40 This results in a single equation involving only variable x. 3 x = 7x / 2 - 96; 3 x = 3.5x - 96; 3 x - 3.5x = - 96; -0.5x = -96; x = (-96)/(-0.5) x = 192; So the amount of durians was 192. And the amount of apples was y/2 = 7 * 192 / 2 - 56; y/2 = 1344/2 - 56; y/2 = 672 - 56; y/2 = 616; y = 1232.
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