MO Z8-I-1 2018

Fero and David meet daily in the elevator. One morning they found that if they multiply their current age, they get 238. If they did the same after four years, this product would be 378. Determine the sum of the current ages of Fero and David.

Correct answer:

s =  31

Step-by-step explanation:

$$\begin{gathered} a\cdot (s-a)=238 \\ (a+4)\cdot (s-a+4)=378 \\ as-a^2=238 \\ as-a^2+4a+4s-4a+16=378 \\ as-a^2=238 \\ as-a^2+4s+16=378 \\ 238+4s+16=378 \\ 238+4\cdot s+16=378 \\ 4s=124 \\ s=31 \end{gathered}$$

The equations have the following integer solutions:

a*(s-a)=238
(a+4)*(s-a+4) = 378

Number of solutions found: 2

a₁=14, s₁=31
a₂=17, s₂=31

Calculated by our Diofant problems and integer equations.

Try another example

Related math problems and questions:

• Year 2018
  The product of the three positive numbers is 2018. What are the numbers?
• Two-digit number
  In a two-digit number, the number of tens is three greater than the number of units. If we multiply the original number by a number written in the same digits but in reverse order, we get product 3 478. Find the original number.
• 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. Fina
• Sales of products
  For 80 pieces of two quality products a total sales is 175 Eur. If the first quality product was sold for n EUR per piece (n natural number) and the second quality product after 2 EUR per piece. How many pieces of the first quality were sold?
• All pairs
  Determine all pairs (m, n) of natural numbers for which is true: m s (n) = n s (m) = 70, where s (a) denotes the digit sum of the natural number a.
• Age
  In 1960 my age was equal to the digits sum of the year of my birth. What is my age now?
• The ages
  The ages of the four sons make an arithmetic sequence, the sum of which is the age of the father today. In three years, the father's age will be the sum of the ages of the three eldest sons, and in the next two years and three months, the father's age wil
• 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
• Luggage and air travel
  Two friends traveling by plane had a total of 35 kg of luggage. They paid one 72 CZK and second 108 CZK for being overweight. If only one paid for all the bags, it would cost 300 CZK. What weight of baggage did each of them have, how many kilograms of lug
• Ages 2
  A man's age is 4 times his son's age. After 5 years he will be just twice his son's age, find their ages.
• Four integers
  Fnd four consecutive integers so that the product of the first two is 70 times smaller than the product of the next two.
• Bricks pyramid
  How many 50cm x 32cm x 30cm brick needed to built a 272m x 272m x 278m pyramid?
• Happy marriage
  Jan and Marienka have been living in a happy marriage for several years. Jan's age is written in the same numbers as Marienka only in reverse order. Their ages differ by just a fifth of Marienka's age. Jan is older. How old is Jan and how many are Marienk
• Self-counting machine
  The self-counting machine works exactly like a calculator. The innkeeper wanted to add several three-digit natural numbers on his own. On the first attempt, he got the result in 2224. To check, he added these numbers again and he got 2198. Therefore, he a
• Digit sum
  The digit sum of the two-digit number is nine. When we turn figures and multiply by the original two-digit number, we get the number 2430. What is the original two-digit number?
• Average age
  The average age of all people at the celebration was equal to the number of people present. After the departure of one person who was 29 years old, average age was again equal to the number present. How many people were originally to celebrate?
• Granddaughter
  In 2014, the sum of the ages of Meghan's aunt, her daughter and her granddaughter was equal to 100 years. In what year was the granddaughter born, if we know that the age of each can be expressed as the power of two?