Math test

In mathematics, there were 25 problems of three kinds: light 2 points, medium 3 points, heavy 5 points, the best score is 84 points. How many points did Jane have when she solved all the easy examples, half medium and one-third difficult?

Correct answer:

J =  40

Step-by-step explanation:

$$\begin{gathered} 84=5a+3b+2c \\ 25=a+b+c \\ a>0;b>0;c>0 \\ 3x=a \\ a=6 \\ b=16 \\ c=3 \\ J=5\cdot a\mathrm{/}3+3\cdot b\mathrm{/}2+2\cdot c=5\cdot 6\mathrm{/}3+3\cdot 16\mathrm{/}2+2\cdot 3=40 \end{gathered}$$

Try another example

Related math problems and questions:

• The math test
  The math test contains 20 problems. For each correctly solved problem, the solver gets 3 points, for each incorrectly solved or unsolved problem, 2 points are deducted. Ondrej got 25 points. How many problems did he solve correctly?
• Testing
  Students of high school have 10 points for each good solved task. The wrong answer is deducted by 5 points. After solving 20 tasks, student Michael had 80 points. How many tasks did he solve correctly and how many wrong?
• Math test
  Obelix filled a mathematical test in which he answered 25 questions. For every correct answer, he received 5 points, for each bad answer he had 3 points deducted. Obelix gained 36% of all points in the test. How many questions did he solve correctly?
• Students
  Students solve word problems. They received 3 points for each correctly solved task. Four points were deducted for a task that was not solved or incorrectly solved. Tomas solved a total of 15 tasks and scored 24 points. How many tasks did he solve correct
• Subjects
  Student makes a mathematical task for five minutes and the task from biology in twelve minutes. Another day he have homework in math and biology which consists of eleven tasks together. To do the job took hour and a half. How many tasks maked in each subj
• Test scores
  Jo's test scores on the first four 100 point exams are as follows: 96,90,76, and 88. If all exams are worth the same percent, what is the minimum test score necessary on his last exam to earn an A grade in the class (90% or better)?
• Intelligence test
  Paľo, Jano, Karol, and Rišo were doing an intelligence test. Palo correctly answered half of the questions plus 7 questions, Jano to a third plus 18 questions, Karol to a quarter plus 21 questions and Risho to a fifth plus 25 questions. After the test, Ka
• Test points
  If you earned 80% of the possible 40 points, how many points did you miss to get 100%?
• Math test
  Brayden was solving some math problems for the math team. He answered 2 math problems. Matthew answered 3, John answered 1 reasoning. Matthew 1/2 times as many. Brayden said that 2/6. Is he correct? Why or why not? Be sure to explain your answer.
• Ľé sweets
  There are 20 sweets in the bag. Some are chocolate, other coconuts, and the remaining marzipan. Chocolate is 4 times more than coconut. Marzipan's less than chocolate. How much is in a bag of coconut sweets?
• Perpetrator
  The perpetrator is a number that is smaller than the number 80. It is a multiple of five and it is odd. If we added up the tens and ones of this number we get number 8.
• 9.A
  9.A to attend more than 20 students but fewer than 40 students. A third of the pupils wrote a math test to mark 1, the sixth to mark 2, the ninth to mark 3. No one gets mark 4. How many students of class 9.A wrote a test to mark 5?
• The Chemistry test
  The Chemistry test contained 8 questions, each with 3 points. Peter scored 21 points. How many percent did Peter write a test?
• Motion problem
  From Levíc to Košíc go car at speed 81 km/h. From Košíc to Levíc go another car at speed 69 km/h. How many minutes before the meeting will be cars 27 km away?
• Painters
  15 painters painted fence for 280 minutes. For how many minutes paint half of this fence 12 painters?
• Lunch
  Jane eats whole lunch for the 30 minutes. Which part of the lunch is eaten in 180 seconds?
• Divisibility
  Determine all divisors of number 84.