Cups

We have three cups. In the cups we had fluid and boredom we started to shed.

1 We shed one-third of the fluid from the second glass into the first and third.
2 Then we shed one quarter cup of liquid from the first to the second and to the third.
3 Then we shed one-fifth of the liquid from the third to the first cup and to the second.

Finally remained 8, 10 and 7 dl fluids in cups. How many dl of liquid was in the cups originally?

Correct result:

a =  6.5 dl
b =  14.5 dl
c =  4 dl

Solution:

d=a+b/3
e=b/3
f = c+b/3
k = d/2
l = e+d/4
m = f+d/4
x = k+m/5
y = l+m/5
z = m •3/5
x=8
y=10
z = 7

3a+b-3d = 0
b-3e = 0
b+3c-3f = 0
d-2k = 0
d+4e-4l = 0
d+4f-4m = 0
5k+m-5x = 0
5l+m-5y = 0
3m-5z = 0
x = 8
y = 10
z = 7

a = 13/2 = 6.5
b = 29/2 = 14.5
c = 4
d = 34/3 ≈ 11.333333
e = 29/6 ≈ 4.833333
f = 53/6 ≈ 8.833333
k = 17/3 ≈ 5.666667
l = 23/3 ≈ 7.666667
m = 35/3 ≈ 11.666667
x = 8
y = 10

Our linear equations calculator calculates it.

Try another example

Showing 0 comments:

Next similar math problems:

• Apples 2
  How many apples were originally on the tree, if the first day fell one third, the second day quarter of the rest and on tree remained 45 apples?
• Milk
  There were 22 liters of milk in three containers. There was 6 liters more in the first container than in the second. After pouring 5 liters from the first container into the third container, the same quantity of milk is in the second and third container.
• Boxes
  200 boxes have been straightened in three rows. The first was 13 more than in the second, and in the second was one fifth more than in the third one. How many boxes are in each row?
• Alloy
  The first alloy is a mixture of two metals in the ratio 1:2, the second is a mixture of same metals in the ratio 2:3. At what ratio we have these two alloys put into the furnace to obtain a new metal alloy with ratio 17:27? (All three ratios correspond to
• Sales stores
  The first sales store passed the 1/3 and the second 2/5 of the total amount of goods.In third store passed the 2/3 rest of the goods. The remaining 40 kg of goods put into fourth store. How many kilograms of goods pass to a third store?
• Ravens
  On two trees sitting 17 ravens. If 3 ravens flew from first to second tree and 5 ravens took off from second tree then the first tree has 2 times more ravens than second tree. How many ravens was originally on every tree?
• Three piles
  100 kg of sugar we divide into three piles. The first pile is small. If we added to second 2 kg of sugar it would have 25% more sugar than the first pile. If we added to third pile 3 kg of sugar it would have 20% more sugar than the 2nd pile. How many kil
• Summands
  We want to split the number 110 into three summands so that the first and the second summand are in the ratio 4: 5, and the third with the first are in ratio 7: 3. Calculate the smallest of the summands.
• Glass with icecream
  We have 6 kinds of ice cream and 5 kinds of fruit. We put 3 cups of ice cream and 2 fruits into each glass. How many can unique decorated glasses be?
• Seamstress
  The seamstress cut the fabric into 3 parts. The first part was the eighth fabric, the second part was three-fifths of the fabric and the third part had a length of 66 cm. Calculate the original length of the fabric.
• Z9-I-4
  Kate thought a five-digit integer. She wrote the sum of this number and its half at the first line to the workbook. On the second line wrote a total of this number and its one fifth. On the third row she wrote a sum of this number and its one nines. Final
• Shop stores
  Workers untied fruit to stores. In the first quarter shipments, in the second fifth shipment, in the third two-fifths of the rest and in the fourth 231 kilograms. How many fruits were together?
• Stamps and albums
  Michail has in three albums stored 170 stamps. In the first album, there are 14 more than in the second and in the second is by 1/5 less than in the third. How many stamps are in the first album?
• Lemonade
  How many 1/4 cup servings are in 2 and 1/3 cups of lemonade?
• 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.
• Sisters
  Sisters Janka and Danka are saved together 220 CZK. On a trip to Janka wants to take a fifth of her savings and Danka quarter. Then they will have 50 CZK on the trip. How much money saved Janka and Danka?
• Gasoline
  35 l of gasoline is to be divided into four canisters so that in the third canister was 5 l less than the first canister, the fourth canister 10 l more than in the third canister and the second canister half what in the first canister. How many liters of