System of equations + fractions - practice problems
Number of problems found: 163
- Violin and dance lesson
Each week, Nina takes a violin lesson and a dance lesson. The dance lesson costs ⅔ as much as the violin lesson, and the combined cost is $75. Which systems of equations could be used to find d, the cost of the dance lesson in dollars, and v, the cost of - The sum 40
The sum of the two numbers is 75. If the smaller number is 20 more than 1/5 of the larger number, find those two numbers. The large number is x, and the small number is y. - A man 14
A man gave 1/3 of his wealth to his wife, 2/3 of the remaining to his daughter, and divided the remaining between his two sons equally. If the daughter received Rs.3000000 more than one of the sons, find the value of the father's property. - There 33
There is a number that is three-fifths the total of the other number. When four is added to one of the numbers, their sum will be equal to the other number. There are two pairs of numbers that satisfy these descriptions. What are they?
- Xero had
Xero had a piece of ribbon. He used 0.4 of it to tie 2 small boxes and 2 large boxes. The length of ribbon needed for a large box is 3 times the length of ribbon needed for a small box. Xero used 5/6 of the remaining ribbon to decorate the presents. a) Wh - Peter 16
Peter travels to his uncle's home, 30 km away from his place. He cycles for 2/3 of the journey before the cycle develops a mechanical problem, and he has to push it for the rest of the journey. If he is cycling 10 km per hour faster than his walking speed - The sum 31
The sum of two fractions is 13 3/4. Their difference is 8 1/5. What are fractions? - Children 82437
If 3 boys were added to the eighth grade, 50% of the class would be boys. If, on the other hand, 3 girls were added, they would make up 7/12 classes. How many children are there in the class? - Apprentices 80561
The master produced a quarter more products than one of his apprentices. Together they produced 45 products. How many products did the apprentice make, and how many did the master make?
- Equations: 80499
In the field of real numbers, solve the system of equations: 2x + ⌊y⌋ = 2022, 3y + ⌊2x⌋ = 2023. (⌊a⌋ denotes the (lower) integer part of the real number a, i.e., the largest integer not greater than a., E.g., ⌊1.9⌋ = 1 and ⌊−1.1⌋ = −2.) - Find k
Find k so that the terms k-3, k+1, and 4k-2 form a geometric sequence. Show your solution. - Pasture 79214
I need to find out the number of bulls in the third period. In the first period, 12 bulls grazed on 3 and 1/3 ha for 4 weeks. In the second period, 21 bulls graze on 10 ha for 9 weeks. How many bulls in the third period graze for 24ha and 18 weeks? The pa - Cows and pigs
There are 3/4 as many cows as pigs on an animal farm. If there are 35 pigs and cows on the farm, how many of them are pigs? - 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
- 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 - Pre-stocking 74604
They delivered potatoes, cabbage, and carrots to the vegetable shop for winter pre-stocking. 2/7 of the total amount is carrots, 1/3 is cabbage, and the rest is potatoes. Carrots are 10 kg less than cabbage. How many kilograms of potatoes do they have in - Determine 73454
The volume of the cut cone is V = 38000π cm³. The radius of the lower base is 10 cm larger than the radius of the upper base. Determine the radius of the base if height v = 60 cm. - The probability
The probability that a life bulb will have a lifetime of more than 682 hours is 0.9788. The probability that a bulb will have a lifetime of more than 703 hours is 0.0051. Find the probability that a bulb will last for more than 648 hours. - Calculate 70804
The garden is a right triangle fenced with a 364 m fence length. The shorter slope of the triangle is 26 m long. Calculate the area of this garden.
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