System of equations - 7th grade (12y) - math problems
Number of problems found: 177
Half a kilogram of pork and three-quarters of a kilogram of beef cost total 5.1 USD. One-quarter of a kilogram of beef and 1 kilogram of pork cost 4.9 USD. Find the price of 1 kg of each type of meat.
Of the girls who attend primary school are 30% blondes and 70% brunette. 81% blondes and 19% brunette has blue eyes. How many girls attending school altogether if 470 girls has blue eyes?
- Rectangles - sides
One side of the rectangle is 10 cm longer than second. Shortens longer side by 6 cm and extend shorter by 14 cm increases the area of the rectangle by 130 cm2. What are the dimensions of the original rectangle?
- Water pool
Pool with volume 990hl completely filled, if water flows by one tap 8 hours and by second tap 6 hours. First tap give 10hl more than second per hour. How many hl flows in each of them in an hour?
- Passenger car and truck
From Kutna Hora left at 11:00 clock a truck at 60 km/h. At 12:30 behind him started passenger car at average speed 80 km/h. At what time and how far from Kutna Hora overtake a passenger car truck?
- Homework - jumps
Sasha jumped 121 cm Peter 4 cm more than Jirka. Jirka 6 cm less than Misha. Misha 7 cm less than Filip and Filip half as much Sasha and Petr together. How far each jumped?
Mother and Kate together weigh 24.5 kg more than the father. Father weighs 7.6 kg more than mother. Father weight 44.8 kg more than Kate. Determine weights of father mother and Kate.
Cyclist started out of town at 19 km/h. After 0.7 hours car started behind him in the same direction and caught up with him for 23 minutes. How fast and how long went car from the city to caught cyclists?
- Bonbons 2
Kilo sweets will cost 260 CZK. The first type has a price per 320 kg, the second type 240 CZK per kg. How many kilos of both kinds of sweets need to prepare a 35 kg mixture ?
Mr. Billy calculated that excavation for a water connection digs for 12 days. His friend would take 10 days. Billy worked 3 days alone. Then his friend came to help and started on the other end. On what day since the beginning of the excavation they met?
- Pedestrian up-down hill
Pedestrian goes for a walk first at the plane at 4 km/h, then uphill 3 km/h. Then it is in the middle of the route, turns back, and goes downhill at speed 6 km/h. The total walk was 6 hours. How many kilometers went pedestrian?
Daniela and Michael would jointly dug potatoes for 7.5 hours. But if Daniela was working alone she would take 2.5 hours more as if he were working with Michael. Determine how much for the work done by Michael himself and how much Daniela herself.
- Train from Brno
First train started from Brno at 8 am at 60 km per hour. Second train started from Opava at 7 o'clock at the speed of 40 kilometers per hour. In how many hours and how far from cities trains meet when the distance of cities is 200 kilometers.
From two different locations distant 232 km started against car and bus. The car started at 5:20 with average speed 64 km/h. Bus started at 7:30 with average speed 80 km/h. When they meet? How many kilometers went the bus?
- Christmas or Easter
Please calculate this example by the Venn equation. They asked 73 students whether they like Christmas or Easter. 34 of them like one of the holidays. 39 loves Easter. There are twice as many students who wish both holidays than those who only love Easter
- 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?
- Train from Prague
First train from Prague started at 8:00 hour at 40 kilometers per hour. Train from Ostrava started at 9:20 at 80 km per hour. In how many hours and how far from cities with trains meet if the distance of cities is 400 km.
- Rings groups
27 pupils attend some group; dance group attends 14 pupils, 21 pupils sporty group and dramatic group 16 pupils. Dance and sporting attend 9 pupils, dance and drama 6 pupil, sporty and dramatic 11 pupils. How many pupils attend all three groups?
- Guess a fraction
Tom was asked to guess a fraction. The sum of 1/2 the numerator and 1/3 of its denominator is 30. If Tom subtracts 36 from its denominator, the fraction becomes 1/3. What is the fraction that Tom was asked to guess? (Leave your answer in simplest form)
The farm bred turkeys, geese, hens and chickens. Everything is 400. Turkeys and geese a hen are 150. No hen has more than one chicken, but some hens has no chick. Half of them is also a quarter of the chickens. When the turkey subtracting 15, we get 75. H
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