Question

PLEASE ANSWER ASAP!!

A social studies test contains geography and history problems. Geography problems are worth 5 points each and history problems are worth 15 points each. You can do a geography problem in 1 minute and a history problem in 5 minutes. You have an hour to take the test and may answer no more than 40 problems. Assuming you answer all the problems
attempted correctly, (a) how many of each type of problem must you do to earn the highest score? (b) what would the resulting highest score be?​

Answer 1

5history problem and 35 geography

the highest score would be 250

Answer 2

5 history, 35 geography,

250 points

Explanation:

Geography - g= 5 points = 1 min

History - h= 15 points = 5 min

In terms of time a minute of geography problem worth 5 points whilst a minute of history problem worth 3 points

Time limitation is an hour, problem limitation is 40 problems:

• g+h≤40 and g+5h≤60

comparing the 2 inequalities:

• 4h≤20 ⇒ h≤5

So, maximum 5 history problems, then min 35 of geography problems

Then max score would be:

• 35*5+5*15= 250