Oranges

Mother divided her three children's oranges in a ratio of 6:5:4. Two children gave 45 oranges. How many oranges were there?

Correct result:

n =  75

Solution:

$$\begin{gathered} a:b:c=6+5+4 \\ a+b=45\mathrm{\mid }\mathrm{\mid }b+c=45\mathrm{\mid }\mathrm{\mid }c+a=45 \\ {k}_1={\displaystyle \frac{6}{6+5+4}}={\displaystyle \frac{2}{5}}=0.4 \\ {k}_2={\displaystyle \frac{5}{6+5+4}}={\displaystyle \frac{1}{3}}\doteq 0.3333 \\ {k}_3={\displaystyle \frac{4}{6+5+4}}={\displaystyle \frac{4}{15}}\doteq 0.2667 \\ {q}_1=k_1+k_2=0.4+0.3333={\displaystyle \frac{11}{15}}\doteq 0.7333 \\ {q}_2=k_1+k_3=0.4+0.2667={\displaystyle \frac{2}{3}}\doteq 0.6667 \\ {q}_3=k_3+k_2=0.2667+0.3333={\displaystyle \frac{3}{5}}=0.6 \\ {n}_1=45\mathrm{/}{q}_1=45\mathrm{/}0.7333={\displaystyle \frac{675}{11}}\doteq 61.3636 \\ {n}_2=45\mathrm{/}{q}_2=45\mathrm{/}0.6667={\displaystyle \frac{135}{2}}=67.5 \\ {n}_3=45\mathrm{/}{q}_3=45\mathrm{/}0.6=75 \\ n=n_3=75 \\ a=k_1\cdot n=0.4\cdot 75=30 \\ b=k_2\cdot n=0.3333\cdot 75=25 \\ c=k_3\cdot n=0.2667\cdot 75=20 \\ n=75 \end{gathered}$$

Try another example

Showing 0 comments:

Next similar math problems:

• Boats
  Three-quarters of boats are white, 1/7 are blue and 9 are red. How many boats do we have?
• Collection of stamps
  Jano, Rado, and Fero have created a collection of stamps in a ratio of 5: 6: 9. Two of them had 429 stamps together. How many stamps did their shared collection have?
• Chickens and rabbits
  In the yard were chickens and rabbits. Together they had 27 heads and 86 legs. How many chickens and how many rabbits were in the yard?
• 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?
• Soaps
  Each box has the same number of soaps. A quarter of all boxes contain only white soaps, and in each of the remaining 120 boxes there are always half the white soaps and half the green. White soaps total 1200. (a) the number of all soap boxes; (b) the smal
• Lookout tower
  How high is the lookout tower? If each step was 3 cm lower, there would be 60 more of them on the lookout tower. If it was 3 cm higher again, it would be 40 less than it is now.
• Sea water
  Mixing 62 kg of sea water with 84 kg rainwater is created water containing 3.1% salt. How many percent sea water contains salt?
• Two cars
  Two cars started against each other at the same time to journey long 346 km. The first car went 53 km/h and the second 53 km/h. What distance will be between these cars 20 minutes before meet?
• Four integers
  Fnd four consecutive integers so that the product of the first two is 70 times smaller than the product of the next two.
• Digit sum
  The digit sum of the two-digit number is nine. When we turn figures and multiply by the original two-digit number, we get the number 2430. What is the original two-digit number?
• Library
  New books were purchased for the library. Five-eighths were professional books, one-fifth were encyclopedias, and 231 books were dictionaries. How many professional books were there?
• Family
  Son is 3/5 smaller than the mother. Mother is 99 cm higher than the son. How tall is the mother?
• Together
  If 8 men, 10 women, 16 children collects ₹1024 in 4 days, how many days will be required for 6 men, 5 women and 4 boys to collect ₹768? (₹ is Indian Rupee)
• Clothes
  Danka and Janka collect clothes. Danka had 9 more than Janka, so she gave her 7. Which now has more cloth and how many?
• Pupils
  There are 32 pupils in the classroom, and girls are two-thirds more than boys. a) How many percents are more girls than boys? Round the result to a whole percentage. b) How many are boys in the class? c) Find the ratio of boys and girls in the class. Writ
• Geography tests
  On three 150-point geography tests, you earned grades of 88%, 94%, and 90%. The final test is worth 250 points. What percent do you need on the final to earn 93% of the total points on all tests?
• Rectangular cuboid
  The rectangular cuboid has a surface area 5334 cm², its dimensions are in the ratio 2:4:5. Find the volume of this rectangular cuboid.