Two fifth-graders teams competing in math competitions - in Mathematical Olympiad and Pytagoriade. Of the 33 students competed in at least one of the contest 22 students. Students who competed only in Pytagoriade was twice more than those who just competed in the Mathematical Olympiad. Students who competed in both competitions was 4 times more than those who only competed in Pytagoriade.

a) How many students competed in both competitions?
b) How many students competed in just one competition?
c) How many students competed in no more than one competition?

Result

a =  16
b =  6
c =  17

Solution:

p+a+o = 22
p = 2 o
a = 4p
b = p+o
c = 33-a

a+o+p = 22
2o-p = 0
a-4p = 0
b-o-p = 0
a+c = 33

a = 16
b = 6
c = 17
o = 2
p = 4

Calculated by our linear equations calculator.

Leave us a comment of this math problem and its solution (i.e. if it is still somewhat unclear...): Be the first to comment! To solve this verbal math problem are needed these knowledge from mathematics:

Do you have a linear equation or system of equations and looking for its solution? Or do you have quadratic equation?

Next similar math problems:

1. Two numbers We have two numbers. Their sum is 140. One-fifth of the first number is equal to half the second number. Determine those unknown numbers.
2. Families In class we investigated how many children have family in which its live. How many% of pupils live in families with more than two children? If five families each have one child in 9 families have 2 children, in 5 families have 3 children, in 2 families ha
3. Find x Solve: if 2(x-1)=14, then x= (solve an equation with one unknown)
4. Three friends The three friends spent 600 KC in a teahouse. Thomas paid twice as much as Paul. Paul a half less than Zdeněk. How many each paid?
5. Three days During the three days sold in stationery 1490 workbooks. The first day sold about workbooks more than third day. The second day 190 workbooks sold less than third day. How many workbooks sold during each day?
6. School year At the end of the school year has awarded 20% of the 250 children who attend school. Awat got 18% boys and 23% of girls. Determine how many boys and how many girls attend school.
7. Candy Peter had a sachet of candy. He wanted to share with his friends. If he gave them 30 candies, he would have 62 candies. If he gave them 40 candies, he would miss 8 candies. How many friends did Peter have?
8. Borrowed book Jane must as soon as possible return a borrowed book. She figured that when she read 15 pages a day return book in time. Then she read 18 pages a day and then return the book one day before. How many pages should have a book?
9. Parking 120 vehicles parking on the morning. Pasenger car is charged 20 CZK, 50 CZK per bus. The guard collected for parking 2640 CZK in total. How many cars and how many buses stood in the parking?
10. Hotel rooms In the 45 rooms, there were 169 guests, some rooms were three-bedrooms and some five-bedrooms. How many rooms were?
11. Belgium vs Italy Belgium played a match with Italy and Belgium win by 2 goals. The match fell a total 6 goals. Determine the number of goals scored by Belgium and by Italy.
12. Equation Solve the equation: 1/2-2/8 = 1/10; Write the result as a decimal number.
13. Three workers Three workers were rewarded CZK 9200 and the money divided by the work they have done. First worker to get twice than the second, the second three times more than the third. How much money each worker received?
14. Tram In the three-part tram went 206 passengers in front of others, 226 after others and in the middle half of all. How many passengers went in tram total?
15. Spain vs USA Spain lost to the US by 4 goals. In the match total fell 10 goals. How many goals gave the Spain and how the United States?
16. Classroom There are eighty more girls in the class than boys. Boys are 40 percent and girls are 60 percent. How many are boys and how many girls?
17. Norm Three workers planted 3555 seedlings of tomatoes in one dey. First worked at the standard norm, the second planted 120 seedlings more and the third 135 seedlings more than the first worker. How many seedlings were standard norm?