# System of equations - math word problems

1. Banknotes
\$ 1390 was collected. How much was in \$20 notes and how many in \$50 notes in that order? How many solutions exists?
2. Cyclist
Cyclist rode two-fifths of the way the first day. The second day drove 5 km less while traveled three-eighths of route. How many kilometers does he have to finish target?
3. Shoes and slippers
Shoes were three times as many as slippers. If shoes were cheaper by 120, it would be twice as expensive as slippers. How much cost shoes and how much slippers?
4. Three ints
The sum of three consecutive integers is 2016. What numbers are they?
5. Bus stop
Determine at what time the bus leaves from the bus stop outside the village, if you know that when you leave home at 8:00 and go at speed 3 km/h, you come to a stop 9 minutes after the departure of the bus, and when you go speed at 4 km/h, you come to the
6. Weights
Marry and John together weighing 49 kg. Their weights are in ratio 1:6. Determine their weights.
7. Rectangle - sides 4
Perimeter of the rectangle is 72 cm. Calculate the length of the sides that are in the ratio 3:5.
8. Barrel 4
Barrel of water weighs 63 kg. After off 75% water, the weight of the barrel with water is 21 kg. How many kg weigh empty barrel and how many kgs water in it?
9. Three numbers
What is three numbers which have the property: the sum of the reciprocals of the first and second numbers is 12/7, the first and third 11/24 and the second and the third 3/8.
10. Truck PRG-BA
Truck driving on highway from Prague to Bratislava at average speed of 72 km/h. At the moment when the truck passes 54 kilometer from Prague passenger car departs from Prague which travel to Bratislava at speed 90 km/h. When and where (at waht highway ki
11. Savings 2
Jozef and Michael saved 46 euros together. Michael saved 22 euros more than Jozef. How much did save each of them?
12. Distance between two cities
Car went from A to B 4h. On the way back, the car was up 15km / h faster. The return trip took 48 minutes. Shorter than the way there. Find the distance of the cities A and B.
13. Saving
The boy has saved 50 coins € 5 and € 2. He saved € 190. How many were € 5 and how many € 2?
14. Cork and swimming
If a person weighs 80 kg, how many kilograms of cork must take swimming belt to use it to float on water? The density of the human body is 1050kg/m3 and cork 300kg/m3. (Instructions: Let the human body and cork on a mixture that has a density of 1000kg/
15. AP - basics
Determine first member and differentiate of the the following sequence: a3-a5=24 a4-2a5=61
16. Euros
Peter, Jane and Thomas have together € 550. Tomas has 20 euros more than Jane, Peter € 150 less than Thomas. Determine how much has each of them.
17. Isosceles trapezoid
Perimeter of the isosceles trapezoid is 48 cm. One side is two times greater than the second side. Determine the dimensions of the trapezoid.
18. Coffee
Coffee merchant has coffee robusta and arabica species. 1 kg Robusta worth 450 CZK, Arabica 1 kg is 300 CZK more expensive. Calculate how many kilograms of Robusta and Arabica will need to produce 30 kg of the mixture so that the mixture cost is 490 CZK p
19. Land areas
Two land areas is 244 m2. The first parcel is 40 m2 less than twice of the second one. What have acreage of each parcel?
20. Triangle - is RT?
Triangle has a circumference of 90 cm. Side b is 1 cm longer than c, side c is 31 cm longer than side a. Calculate the length of sides and determine whether triangle is a right triangle.

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