Posted by **CJ** on Monday, November 12, 2007 at 4:02pm.

you are about to take a test that contain questions of type A worth 4 points and of type B worth 7 points. You must answer at least 5 of type A and 3 of type B, but time restricts answering more than 10 of either type. In total, you can answer no more than 18. How many of each type of question can you answer, assuming all of your answers are correct, to maximize your score? What is the maximum score?

- Algebra -
**Michael**, Monday, November 12, 2007 at 4:28pm
You want to answer as many of type B as possible because they're worth the most points.

10*7 = 70

That leaves eight questions of type A that you can answer.

8*4 = 32

70 + 32 = 102

- Algebra -
**Reiny**, Monday, November 12, 2007 at 4:29pm
let the number of questions answered from part A be x

let the number of questions answered from part B be y

we have 3 main conditions:

x ≤ 10

y ≤ 10 and

x+y ≤ 18

also we have x>5 and y>3

sketch this on a graph and any point with integer coordinates in the first quadrant that satisfies these conditions would be a possible "test".

Then Marks = 4x + 7y

this can be represented by a straight line with slope -4/7.

we want this line to be as far away from the origin as possible, (highest mark), but still be in contact with the region we have defined.

notice the slope of x+y=18 is -1 which is 45º to the left, while a slope of -4/7 is a line not yet 45º

so marks=4x+7y would still touch our region at the point (10,18), namely the intersection of the boundaries x+y=18 and y=10

so you should answer 8 questions form part A and 10 questions from part B

for a total score of 102

## Answer this Question

## Related Questions

- Math Algebra - Question:: You are about to take a test that contains questions ...
- Algebra - An Algebra I test contains 30 questions. Some of the questions are ...
- math - An Algebra I test contains 40 questions. Some of the questions are worth ...
- Algebra - A history test is to have 20 questions in which some are multiple ...
- math - algebra in 8th your teacher is giving you a test worth 100 points ...
- mathematics - seeds of type A and type B are sold in packets, each must contain ...
- Algebra - Your teacher is giving you a test worth 100 points containing 40 ...
- algebra - On a trivia game show, a contestent will answer 21 questions. A ...
- math - Mr. Noonan told Vic that his test had 38 problems worth a total of 100 ...
- math help - I need help solving this math problem, please: Problem: Angela's ...

More Related Questions