# 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 result:

s =  31

#### Solution:

$a \cdot \ (s-a)=238 \ \\ (a+4) \cdot \ (s-a+4)=378 \ \\ \ \\ as-a^2=238 \ \\ as-a^2+4a +4s-4a+16=378 \ \\ \ \\ as-a^2=238 \ \\ as-a^2+4s+16=378 \ \\ \ \\ \ \\ 238 + 4s + 16=378 \ \\ \ \\ 238 + 4 \cdot \ s + 16=378 \ \\ \ \\ 4s=124 \ \\ \ \\ s=31$

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=31a2=17, s2=31

Calculated by our Diofant problems and integer equations. We would be pleased if you find an error in the word problem, spelling mistakes, or inaccuracies and send it to us. Thank you! Tips to related online calculators
Looking for help with calculating roots of a quadratic equation?
Do you have a linear equation or system of equations and looking for its solution? Or do you have quadratic equation?
Do you solve Diofant problems and looking for a calculator of Diofant integer equations?
Do you want to convert time units like minutes to seconds?

## Next similar math problems:

• Substitution solve equations by substitution: x+y= 11 y=5x-25
• Six years In six years Jan will be twice as old as he was six years ago. How old is he?
• Viju viju has 40 chickens and rabbits. If in all there are 90 legs. How many rabbits are there with viju??
• 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?
• 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?
• 13 tickets A short and long sightseeing tour is possible at the castle. Ticket for a short sightseeing circuit costs CZK 60, for a long touring circuit costs CZK 100. So far, 13 tickets have been sold for 1140 CZK. How much did you pay for tickets for a short tour?
• Large family I have as many brothers as sisters and each my brother has twice as many sisters as brothers. How many children do parents have?
• Football match 4 In a football match with the Italy lost 3 goals with Germans. Totally fell 5 goals in the match. Determine the number of goals of Italy and Germany.
• Father and son When I was 11, my father was 35 years old. Today, my father has three times more years than me. How old is she?
• Summerjob Three students participated in the summerjob. Altogether they earn 1780, -. Peter got a third less than John and Paul got 100,- more than Peter. How much got every one of them?
• Jane plants Jane plants flowers in the garden. If she planted 12 every hour instead of 9 flowers, she would finish with the job an hour earlier. How many flowers does she plant?
• Scratches The ticket seller sold 1,280 scratch cards in three days. On the second day, he sold 90 tickets less than on the first day, on the third day he sold 1.5 times more tickets than on the second day. How many tickets did he sell on the third day?
• Mother and son Mother is four times older than her son. In 16 years, the son will be two times younger than his mother. How many years are mother and son?
• Peter and Paul Peter and Paul together have 26 years. Four years ago, Paul was twice older than Peter. How much is Paul and how much Peter?
• Tunnels Mice had built an underground house consisting of chambers and tunnels: • each tunnel leading from the chamber to the chamber (none is blind) • from each chamber lead just three tunnels into three distinct chambers, • from each chamber mice can get to any
• Walnuts x walnuts were in the mission. Dano took 1/4 of nuts Michael took 1/8 from the rest and John took 34 nuts. It stayed here 29 nuts. Determine the original number of nuts.
• Time passing 6 years ago, Marcela's mother was two times older than her and two times younger than her father. When Marcela is 36, she will be twice as young as her father. How old are Marcela, her father, and mother now?