Dance ensembles

4 dance ensembles were dancing at the festival. None had less than 10 and more than 20 members. All dancers from some of the two ensembles were represented in each dance. First, 31 participants were on the stage, then 32, 34, 35, 37, and 38. How many dancers did the individual ensembles have?

Correct answer:

a =  14
b =  17
c =  18
d =  20

Step-by-step explanation:

$$\begin{gathered} 10<a,b,c,d<20 \\ a=14 \\ b=17 \\ c=18 \end{gathered}$$

$$\begin{gathered} d=20 \\ \text{ Verifying Solution: } \\ {s}_1=a+b=14+17=31 \\ {s}_2=a+c=14+18=32 \\ {s}_3=a+d=14+20=34 \\ {s}_4=b+c=17+18=35 \\ {s}_5=b+d=17+20=37 \\ {s}_6=c+d=18+20=38 \end{gathered}$$

Try another example

Related math problems and questions:

• The raw
  The raw data presented here are the scores (out of 100 marks) of a market survey regarding the acceptability of new product launched by a company for random sample of 50 respondents: 40 45 41 45 45 30 30 8 48 25 26 9 23 24 26 29 8 40 41 42 39 35 18 25 35
• N percentille problem
  Here is a data set (n=117) that has been sorted. 10.4 12.2 14.3 15.3 17.1 17.8 18 18.6 19.1 19.9 19.9 20.3 20.6 20.7 20.7 21.2 21.3 22 22.1 22.3 22.8 23 23 23.1 23.5 24.1 24.1 24.4 24.5 24.8 24.9 25.4 25.4 25.5 25.7 25.9 26 26.1 26.2 26.7 26.8 27.5 27.6 2
• The average
  The average of one set of 4 numbers is 35. The average of another set of number is 20. The average of the numbers in the two sets is 30. How many numbers are there in the other set?
• Chickens and rabbits
  In the yard were chickens and rabbits. Together they had 18 heads and 56 legs. How many chickens and how many rabbits were in the yard?
• Percents - easy
  How many percent is 432 out of 434?
• Range, mean, median
  Ages of 7 employees in an office are given below 32, 42, 30, 32, 33, 23, 32 Find a) Range b) Mean c) Median
• Speed of Slovakian trains
  Rudolf decided to take the train from the station 'Ostratice' to 'Horné Ozorovce'. In the train timetables found train Os 5409 : km 0 Chynorany 15:17 5 Ostratice 15:23 15:23 8 Rybany 15:27 15:27 10 Dolné Naštice 15:31 15:31 14 Bánovce nad Bebravou 15:35 1
• Triangle
  Determine if it is possible to construct a triangle with sides 28 31 34 by calculation.
• Divisible by 5
  How many three-digit odd numbers divisible by 5, which are in place ten's number 3?
• Dinosaurs
  More than 30 and less than 60 dinosaurs have met at the pond. A quarter of them bathed and 1/7 saws, and the rest gripped. How many were at the pond? How many were there?
• Pytagoriade
  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 were twice more than those who just compet
• 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?
• Numbers
  By how many is the difference of numbers 8 and 34 less than its product?
• Quotient
  Find quotient before the bracket - the largest divisor 51 a + 34 b + 68 121y-99z-33
• Complaints
  The table is given: days complaints 0-4 2 5-9 4 10-14 8 15-19 6 20-24 4 25-29 3 30-34 3 1.1 What percentage of complaints were resolved within 2weeks? 1.2 calculate the mean number of days to resolve these complaints. 1.3 calculate the modal number of day
• Motion
  Cyclist started at 9:00 from point S to point T. After 10 minutes, followed him at the same speed the second cyclist. Walker, which went from T to S, started at 9:35. After 71 minutes he met the first cyclist and after next 8 minutes the second cyclist. D
• Sum of fall dices
  What is the probability that the sum of 9 will fall on a roll of two dice? Hint: write down all the pairs that can occur as follows: 11 12 13 14 15. . 21 22 23 24. .. . 31 32. .. . . . . . .. . 66, count them, it's the variable n variable m: 36, 63,. .. .