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.

Correct result:

a =  24
b =  30
c =  56

Solution:

a+b+c=110
a=4/5•b
c=7/3•a

a+b+c = 110
5a-4b = 0
7a-3c = 0

a = 24
b = 30
c = 56

Our linear equations calculator calculates it.

Try another example

Showing 0 comments:

Next similar math problems:

• 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
• Three numbers
  Find three numbers so that the second number is 4 times greater than the first and the third is lower by 5 than the second number. Their sum is 67.
• Summand
  One of the summands is 145. The second is 10 more. Determine the sum of the summands.
• Gasoline canisters
  35 liters of gasoline is to be divided into 4 canisters so that in the third canister will have 5 liters less than in the first canister, the fourth canister 10 liters more than the third canister and the second canister half of that in the first canister
• Ratio of two unknown numbers
  Two numbers are given. Their sum is 30. We calculate one-sixth of a larger number and add to both numbers. So we get new numbers whose ratio is 5:7. Which two numbers were given?
• Warehouses
  To four warehouses is going cement in 25 kg bags. To first one third, to second quarter of the total. The third store got two thirds of the rest, and the last 310 tons came to fourth. How many cement is in all warehouses and how much got every one?
• 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
• Five numbers in ratio
  There are 5 integers that are in the ratio 1: 2: 3: 4: 5. Their arithmetic mean is 12. Determine the smallest of these numbers.
• Reminder and quotient
  There are given numbers A = 135, B = 315. Find the smallest natural number R greater than 1 so that the proportions R:A, R:B are with the remainder 1.
• Triangle in circle
  Vertices of the triangle ABC lies on a circle with radius 3 so that it is divided into three parts in the ratio 4:4:4. Calculate the circumference of the triangle ABC.
• The balls
  You have 108 red and 180 green balls. You have to be grouped into the bags so that the ratio of red to green in each bag was the same. What smallest number of balls may be in one bag?
• Square into three rectangles
  Divide the square with a side length of 12 cm into three rectangles with have the same circumference so that these circumferences are as small as possible.
• Numbers at ratio
  The two numbers are in a ratio 3:2. If we each increase by 5 would be at a ratio of 4:3. What is the sum of original numbers?
• Points
  Gryffindor won 437 points. How many points obtained by each of the faculties if they were split at a ratio of 5: 7: 3: 4?
• Trio ratio
  Hans, Alena and Thomas have a total of 740 USD. Hans and Alena split in the ratio 5: 6 and Alena and Thomas in the ratio 4: 5. How much will everyone get?
• Magic number
  The number 135 split to two addends so that one addend was 30 greater than 2/5 the addend.
• Divide
  Divide substance 110 cm long to two parts so that it first part is 10 cm longer than the second part and one part will be 10 times longer than the second portion. How long the parts will be?