Fractions + system of equations - practice problems - page 6 of 9
Number of problems found: 163
- Boys to girls
The ratio of boys to girls at a party is 3:5. If six more boys arrived and four girls left the party, the ratio of boys to girls would be 5:6. How many people were at the party initially? - Summands
We want to split the number 110 into three summands so that the first and the second summand are in ratio 4:5, and the third with the first are in ratio 7:3. Calculate the smallest summands. - Procedure 34191
Petr got a fifth more than Pavel, Jirka got 100 CZK more than Petr, and Honza got half of what Petr did, so they shared the reward of CZK 2,500. Solution and procedure. - Together 20433
Pavel received half as much money from his parents as Petr and Milan and half as much as Pavel. How much did all the boys get together? The parents gave Milan CZK 1,350.
- Adding
Divide number 135 into two additions so that one adds 30 more than 2/5 of the other. Write the bigger one. - Simultaneously 6563
The fraction will have a value of 3 if we increase the numerator (a) by 1 and simultaneously decrease the denominator (b) by 2. However, if we simultaneously decrease the numerator and the denominator by 1, the fraction will have a value of 1/2. What frac - Alice
Alice spent 5/11 of her money on a backpack. She has 42 dollars left. How much was her backpack? - Summands 66044
Divide the number 6 into three summands x, y, z so that x: y = 4:3, y: z = 1:2. - Equations 5070
Solve in RxRxR a system of 3 linear equations with three unknowns: 1/2 x + 3/4 y = 6z 2x-z = 10 1/2 2z + x = 2y + 7 note : / is a fraction line
- The lengths
The lengths of the twelve poles form an Arithmetic Progression (A. P). If the third pole is 3m and the eighth pole is 5 m, find the (i) Length of the first pole (ii) Sum of the length of the poles - Find k
Find k so that the terms k-3, k+1, and 4k-2 form a geometric sequence. Show your solution. - Tracksuit 5460
The tracksuit became cheaper by 15% later on sale and later by 10%. How many euros did Janka save if she bought this set after the second discount and paid € 45.9? - Received 47171
Four boys shared 100 marbles. The second received 20% more than the first, the third received 20 more bullets than the first, and the fourth received 0.8 times more bullets than the first. How many marbles did each boy get? - Circumference 66134
The isosceles trapezoid ABCD has an area of 36 cm². One of its bases is two times longer than the other. Height is 4 cm. Calculate the circumference of the trapezoid.
- Difference 3101
The difference between the two numbers is 4/3. Specify both numbers if you know that the first number is 50% larger than the second number. - Parking
At a building parking, 245 spaces are for cars, 56 are for vans, and the rest are for buses. If 14% of all parking spaces are for buses, how many parking spaces are there in the building? How many spaces are for buses? - Pupils 6434
There are 25 pupils in every 5th class in the class, 18% of boys and 23% of girls. How many boys are in the class, and how many girls are there? - Five friends
Five friends ate a 12-slice pizza. Samir ate three times as many slices as Joe. Joe ate half as many slices as Emily. Kendra and Fong together ate half a pizza. Kendra ate one-third as many slices as Samir. Fong ate the most slices. What fraction of a piz - Four bicycles
In the department store, they sell bicycles for families with children. Women's bicycles are 10% more expensive than men's, and children's bikes are a third cheaper than women's. The family paid a total of CZK 31,030 for two children's, one man's, and one
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