A person on an exercise regime decides to lose 500 calories in a day. For every 30 mins of exercise he loses 80 calories, bu gains 25 calories per cake that he eats. In the morning he exercises for certain time and eats a certain number of cakes. In the afternoon he exercises for double the time bu…

Question

A person on an exercise regime decides to lose 500 calories in a day. For every 30 mins of exercise he loses 80 calories, bu gains 25 calories per cake that he eats. In the morning he exercises for certain time and eats a certain number of cakes. In the afternoon he exercises for double the time but eats thrice the no of cakes. In the evening he exercises for 1.5 times the time he spends in the morning session and eats 4 times the number of cakes he eats in the morning. Had he not eaten any cake, he would have exceeded his target by 220 calories. If he actually falls short of his target by 180 calories, what is the no of cakes he has eaten in evening??? ANS=8. Please help with the approach

Pv Aaditya · Answer

Let the time for which he exercises in the morning be x minutes and the number of cakes he eats in the morning be y
So, Total calorie gain = -(x/30)*80 + 25y -2*(x/30)*80 + 75y - (3/2)*(x/30)*80 + 100y
= -12x + 200y
Had he not eaten the cake, calorie loss = 12x = 720 => x = 60
In reality, he falls short by 180 calories => -720 + 200y = -320
=> 200y = 400 => y = 2
So, he eats 2*4 = 8 cakes in the evening

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