Jason is on a new exercise regimen. To begin, his trainer does not want him to complete more than a total of 32 lunges and sit-ups. For every lunge that he completes, Jacob burns 30 calories. He burns an additional 20 calories for every sit-up. His goal is to burn at least 770 calories during a workout session. Which is a combination of lunges and sit-ups that Jacob can complete in a session?

19 lunges and 14 sit-ups

18 lunges and 10 sit-ups

12 lunges and 16 sit-ups

14 lunges and 18 sit-ups

Question

Jason is on a new exercise regimen. To begin, his trainer does not want him to complete more than a total of 32 lunges and sit-ups. For every lunge that he completes, Jacob burns 30 calories. He burns an additional 20 calories for every sit-up. His goal is to burn at least 770 calories during a workout session. Which is a combination of lunges and sit-ups that Jacob can complete in a session?

19 lunges and 14 sit-ups

18 lunges and 10 sit-ups

12 lunges and 16 sit-ups

14 lunges and 18 sit-ups

anonymous · Answer

Someone please help me out!=D

whpalmer4 · Answer

Let l be the number of lunges, and s be the number of sit-ups.
l+s <= 32

calories burned will be 30*l + 20*s >= 770

whpalmer4 · Answer

From a test-taking tactic point of view, you can immediately eliminate the first choice, because it is 33 lunges + sit-ups, which violates the l+s <= 32 constraint.

whpalmer4 · Answer

Now you can either do the arithmetic to compute calories for each choice, and pick the right answer, or you can do some algebra.

anonymous · Answer

wait so how to i solve for the right answer?

whpalmer4 · Answer

Okay, that would be the algebra choice!  We'll make our inequalities into equalities, and then check our answer to make sure it still satisfies the inequalities.

$$l+s = 32$$$$30l + 20s = 770$$

Let solve by substitution because we have an easy substitution here.
$$l = 32-s$$$$30(32-s) + 20s = 770$$$$960 -30s + 20s = 770$$$$-10s = -190$$$$s = 19$$
now plug that back into l = 32-s to find the value of l

When you are done, make sure your values still satisfy the original two inequalities.

whpalmer4 · Answer

You'll find that while they satisfy the inequalities, the answer isn't among your choices.  That means the laziest option (do exactly 770 calories worth of work) wasn't the one that he chose.

whpalmer4 · Answer

You'll have to do the arithmetic on each of the choices to see which one works.

anonymous · Answer

yeah cause i did it and the closes i got was 780

whpalmer4 · Answer

(but as we already showed, the first one is not a possibility).  because the value of calories burned is more sensitive to the number of lunges (30 cals per) than situps (20 cals per), I would first check the choice with the largest number of lunges.  if that doesn't give an answer, I would next look at the one with the largest number of situps.  That turns out to be the winner, as you've found.