Question

3) A person on an exercise regime decides to lose 500 calories in a day.Fo
every 30 minutes of exercise he loses 80 calories, but gains 25 calories
per cake that he eats.In the morning he exercises for a certain time and
eats certain number of cakes. In the afternoon he exercises for 1.5 times
he spends in the morning session and eats 4 times the number of cakes
he eats in the morning. In the evening he exercises for double the time as
that of morning and eats thrice the number of cakes that 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, then
what is the number of cakes he has eaten in the evening?

Answer 1

Answer:

Step-by-step explanation:

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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Answer 2

Given : A person on an exercise regime decides to lose 500 calories in a day. For  every 30 minutes of exercise he loses 80 calories, but gains 25 calories  per cake  

To find : what is the number of cakes he has eaten in the evening

Solution:

For every 30 minutes of exercise he loses 80 calories

=> For every minute calorie lost  =  80/30  = 8/3 calories

=> for 60 minutes calories lost = 60 * 8/3  = 160 Calories

Calories lost in 1 hr  = 160 Calories

Calories gain per cake = 25 Calories

Let say in Morning exercise done for T  Hrs

Calories Lost = 160T

Let say in Morning Cake eaten = C

Calories Gain = 25C

in Afternoon  Calories Lost  = 1.5 * 160T =  240T

in afternoon Calories  gain = 4(25C) = 100C

in Evening Calories Lost = 2(160T) = 320T

in Evening Calories Gain =  3(25C)  = 75C

Calories Lost = 160T + 240T + 320T  = 720T

Calories Gain = 25C + 100C + 75C = 200C

Target = 500 Calories Lost

Had he not eaten any cake, he would have exceeded his target

by 220 calories.

=> 720T = 500 + 220

=> 720T = 720

=> T = 1

actually falls short of his target by 180 calories

=> 720T - 200C   = 500 - 180

=> 720  - 200C = 320

=> 200C = 400

=> C = 2

Cakes eaten in evening = 3C  = 3 * 2 = 6  Cake

6 Cakes Eaten in Evening

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