On the meadow grazing horses, cows and sheep, together less than 200. If cows were 45 times more, horses 60 times more and sheep 35 times more than there are now, their numbers would equall. How many
horses, cows and sheep are on the meadow together?

Result

x1 =  85
x2 =  170

#### Solution:

x = a+b+c < 200
b = 45/60 a
c = 45/35 a
a + 45/60 a + 45/35 a < 200
LCD(11, 4560, 4535) = LCM(1, 60, 35) = 22×3×5×7 = 420
11 = 420420
4560 = 315420
4535 = 540420

420 k + 315 k + 540 k < 84000
1275 k < 84000
17 k < 1120

x = 56+42+72 = 170
x = 28+21+36 = 85

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

Do you want to calculate least common multiple two or more numbers? Need help calculate sum, simplify or multiply fractions? Try our fraction calculator.

## Next similar examples:

1. Numbers Determine the number of all positive integers less than 4183444 if each is divisible by 29, 7, 17. What is its sum?
2. Reminder and quotient There are given numbers A = 135, B = 315. Find the smallest natural number R greater than 1 so that the proportions R:A, R:B are with the remainder 1.
3. 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?
4. Sugar - cuboid Pejko received from his master cuboid composed of identical sugar cubes with count between 1000 and 2000. The Pejko eat sugar cubes in layers. The first day eat one layer from the front, second day one layer from right, the third day one layer above. Yet i
5. Z9-I-4 Kate thought a five-digit integer. She wrote the sum of this number and its half at the first line to the workbook. On the second line wrote a total of this number and its one fifth. On the third row she wrote a sum of this number and its one nines. Fi
6. No. of divisors How many different divisors has number ??
7. Birthdate Jane on birthday brought 30 lollipops and 24 chewing gum for their friends. How many friends has, if everyone receives the same number of lollipops and chewing gums? How much chewing gum and lollipops got any friend?
8. Diofant 2 Is equation ? solvable on the set of integers Z?
9. Plumber Plumber had to cut the metal strip with dimensions 380 cm and 60 cm to the largest squares so that no waste. Calculate the length of the sides of a square. How many squares cut it?
10. Seedcake Seedcake costs 44 cents. How many minimum seedcakes we must buy that we can pay in cash only whole euros?
11. Diofant equation In the set of integers (Z) solve the equation: ? Write result with integer parameter ? (parameter t = ...-2,-1,0,1,2,3... if equation has infinitely many solutions)
12. Rectangles How many rectangles with area 3032 cm2 whose sides is natural numbers are?
13. Divisibility Determine the smallest integer which divided 11 gives remainder 4 when divided 15 gives remainder 10 and when divided by 19 gives remainder 16.
14. Lines Five bus lines runs at intervals 3, 6, 9, 12, 15 minutes. In the morning, suddenly start at 4:00. After how many minutes the bus lines meet again?
15. Count of roots How many solutions has equation x. y = 7757 with two unknowns on the set of natural numbers?
16. Segments Line segments 62 cm and 2.2 dm long we divide into equal parts which lengths in centimeters is expressed integer. How many ways can we divide?
17. Tiles The room has dimensions 12 m and 5.6 m. Determine the number of square tiles and their largest possible size to cover them room's floor.