Daughters

The man conducting the census asks a woman to age of three daughters. Woman says when multiply the age getnumber 72; if their ages add up, get a number of our house, as you see. The man says: That is not enough to calculate their ages. She says: my oldest daughter has a cat with a wooden leg. The man replies: So now I know their age.

How old are her daughter?

Correct result:

x =  3
y =  4
z =  6

Solution:

$$\begin{gathered} 72=2\cdot 2\cdot 2\cdot 3\cdot 3=2^3\cdot 3^2 \\ D(72)=\{1,2,3,4,6,8,9,12,18,24,36,72\} \\ 72=3\cdot 4\cdot 6 \\ x<y<z<10 \\ x=3 \\ y=4 \\ z=6 \end{gathered}$$

$y=4$

$z=6$

The equations have the following integer solutions:

x*y*z = 72
x<y
y<z
s = x+y+z
x>0
y>0
z>0

Number of solutions found: 8

s₁=13, x₁=3, y₁=4, z₁=6
s₂=15, x₂=2, y₂=4, z₂=9
s₃=17, x₃=2, y₃=3, z₃=12
s₄=18, x₄=1, y₄=8, z₄=9
s₅=19, x₅=1, y₅=6, z₅=12
s₆=23, x₆=1, y₆=4, z₆=18
s₇=28, x₇=1, y₇=3, z₇=24
s₈=39, x₈=1, y₈=2, z₈=36

Calculated by our Diofant problems and integer equations.

Try another example

Showing 0 comments:

Next similar math problems:

• Combine / add term
  Combine like terms 4c+c-7c
• Product
  Result of the product of the numbers 1, 2, 3, 1, 2, 0 is:
• Addition of Roman numbers
  Added together and write as decimal number: LXVII + MLXIV
• Roman numerals +
  Add up the number writtens in Roman numerals. Write the results as a decimal number.
• Cages
  Honza had three cages (black, silver, gold) and three animals (guinea pig, rat and puppy). There was one animal in each cage. The golden cage stood to the left of the black cage. The silver cage stood on the right of the guinea pig cage. The rat was in th
• Decimal expansion
  Calculate: 2 . 1 + 0 . 10 + 7 . 10000 + 4 . 1000 + 6 . 100 + 0 . 100000 =
• Roman numerals 2+
  Add up the number writtens in Roman numerals. Write the results as a roman numbers.
• Multiples
  What is the sum of the multiples of number 7 that are greater than 30 but less than 56?
• Crocuses
  The garden grow daffodils, crocuses and roses. 1400 daffodils, crocuses is 462 more and roses is 156 more than crocuses. How many are all the flowers in the garden?
• Sick
  Sick Marcel already taken six tablets, which was a quarter of the total number of pills in the pack. How many pills were in the pack?
• Table 3x3
  Table with numbers 3x3 in the first row 66,24,33 in the second row 57,? 19 in the third row 18,45,60 What number comes ar mark ?. Maybe the numbers: 22,46,45,47
• 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?
• 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.
• Travel by bus
  Five girls traveling by bus. Each holds in each hand two baskets. Each basket contains 5 cats. Each cat has 5 kittens. 3 girls getting off the bus and another girl without baskets go on board. The bus control driver. How many legs are in the bus?
• Street numbers
  Lada came to aunt. On the way he noticed that the houses on the left side of the street have odd numbers on the right side and even numbers. The street where he lives aunt, there are 5 houses with an even number, which contains at least one digit number 6
• Five girls
  Five girls traveling by bus. Each holds in each hand two baskets. In each basket are four cats. Each cat has three kittens. Two girls exits bus. How many legs are in the bus?
• The largest number
  Find the largest integer such that: 1. No figures is not repeat, 2. multiplication of every two digits is odd, 3. addition all digits is odd.