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?
• 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?
• Cupcakes 2
  Susi has 25 cupcakes. She gives 4/5. How much does she have left?
• Group
  A group of kids wanted to ride. When the children were divided into groups of 3 children, one remain. When divided into groups of 4 children, 1 remains. When divided into groups of 6 children, 1 remains. After divided into groups of 5 children, no one lef
• Families
  In the class, we investigated how many children have families in which they live. How many % of pupils live in families with more than two children? If five families have one child in 9 families, have 2 children, in 5 families have 3 children, in 2 famili
• Brothers and sisters
  There are 35 children in the class, 23 of them have a brother, and 27 of them have a sister. How many children have both a brother and a sister when there are 5 children in the class who have no brother or sister?
• Fruits
  Amy bought a basket of fruits 1/5 of them were apples,1/4 were oranges, and the rest were 33 bananas. How many fruits did she buy in all?
• Points
  Gryffindor won 437 points. How many points obtained by each of the faculties if they were split at a ratio of 5: 7: 3: 4?
• 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?
• Digits
  How many odd four-digit numbers can we create from digits: 0, 3, 5, 6, 7? (a) the figures may be repeated (b) the digits may not be repeated
• Divisibility
  Determine all divisors of number 84.
• Princess
  Princess has lost 321 beads and Prince George are all trying to find. On the first day he found all but 83 beads. On the second day he found 68 beads. On the third day he found the rest, but the princess had lost 76. How many beads had Princess after the
• Fractions and mixed numerals
  (a) Convert the following mixed numbers to improper fractions. i. 3 5/8 ii. 7 7/6 (b) Convert the following improper fraction to mixed number. i. 13/4 ii. 78/5 (c) Simplify these fractions to their lowest terms. i. 36/42 ii. 27/45 2. evaluate following ex
• 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
• Birthday party
  For her youngest son's birthday party, the mother bought 6 3/4 kg of hotdog and 5 1/3 dozens bread rolls. Hotdogs cost 160 per kilogram, and a dozen bread rolls cost 25. How much did she spend in all?
• 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
• 5 2/5
  5 2/5 hours a week  mathematics,  3 3/4 hours a week   Natural sciences, 4 3/8 hours a week  Technology . how many hours does  he spend on social sciences if he spend 17 1/2 hours a week for the four subject?