Luggage and air travel

Two friends traveling by plane had a total of 35 kg of luggage. They paid one 72 CZK and second 108 CZK for being overweight. If only one paid for all the bags, it would cost 300 CZK. What weight of baggage did each of them have, how many kilograms of luggage could a single passenger carry for free?

Correct result:

a =  16 kg
b =  19 kg
x =  10 kg

Solution:

a+b = 35
a-x = 72p
b-x = 108p
a+b-x = 300p

a+b = 35
a-x = 72•p
b-x = 108•p
a+b-x = 300•p

a+b = 35
a-72p-x = 0
b-108p-x = 0
a+b-300p-x = 0

a = 16
b = 19
p = 1/12 ≈ 0.083333
x = 10

Calculated by our linear equations calculator.

Try another example

Showing 0 comments:

Next similar math problems:

• Three friends
  The three friends spent 600 KC in a teahouse. Thomas paid twice as much as Paul. Paul a half less than Zdeněk. How many each paid?
• Three brothers
  The three brothers have a total of 42 years. Jan is five years younger than Peter and Peter is 2 years younger than Michael. How many years has each of them?
• Collecting day
  At collecting day at school pupils of three classes took total of 1063 kg of paper. Class B collected half more than A Class and class C 55 kg more than B. How many kg of paper collected each class?
• Two melons
  There are 2 melons in the box. Together they weigh 11kg. The weight of green is 3 kg less than three times the weight of yellow. What is the weight of a green melon?
• Two numbers
  We have two numbers. Their sum is 140. One-fifth of the first number is equal to half the second number. Determine those unknown numbers.
• Three days
  During the three days sold in stationery 1490 workbooks. The first day sold about workbooks more than third day. The second day 190 workbooks sold less than third day. How many workbooks sold during each day?
• Hotel rooms
  In the 45 rooms, there were 169 guests, some rooms were three-bedrooms and some five-bedrooms. How many rooms were?
• Barrel 4
  Barrel of water weighs 63 kg. After off 75% water, the weight of the barrel with water is 21 kg. How many kg weigh empty barrel and how many kgs water in it?
• The cube
  The cube and cylinder weigh the same as three 20-gram weights. Three cubes and one cylinder weigh the same as two cylinders and one cube. How many grams does one cube weigh (and one cylinder)?
• Linear system
  Solve this linear system (two linear equations with two unknowns): x+y =36 19x+22y=720
• The dormitory
  The dormitory accommodates 150 pupils in 42 rooms, some of which are triple and some are quadruple. Determine how many rooms are triple and how many quadruples.
• Tunnels
  Mice had built an underground house consisting of chambers and tunnels: • each tunnel leading from the chamber to the chamber (none is blind) • from each chamber lead just three tunnels into three distinct chambers, • from each chamber mice can get to any
• Theatro
  Theatrical performance was attended by 480 spectators. Women were in the audience 40 more than men and children 60 less than half of adult spectators. How many men, women and children attended a theater performance?
• Equations
  Solve following system of equations: 6(x+7)+4(y-5)=12 2(x+y)-3(-2x+4y)=-44
• Mushrooms
  Eva and Jane collected 114 mushrooms together. Eve found twice as much as Jane. How many mushrooms found each of them?
• Trees
  Along the road were planted 250 trees of two types. Cherry for 60 CZK apiece and apple 50 CZK apiece. The entire plantation cost 12,800 CZK. How many was cherries and apples?
• Equations - simple
  Solve system of linear equations: x-2y=6 3x+2y=4