Four bicycles

In the department store, they sell bicycles for families with children. Women's bicycles are 10% more expensive than men's, and children's bikes are a third cheaper than women's. The family paid a total of CZK 31,030 for two children's, one man's, and one woman's bike. How many crowns did each round cost?

Correct answer:

d =  9570 Kc
p =  8700 Kc
c =  6380 Kc

Step-by-step explanation:

p1=100%+10%=1+10010=1.1  d=p1 p c=dd/3 2c+p+d=31030 d=1.1 p c=dd/3 2c+p+d=31030  d=1.1 p c=dd/3 2 c+p+d=31030  d1.1p=0 3c2d=0 2c+d+p=31030  Pivot:Row1Row2 3c2d=0 d1.1p=0 2c+d+p=31030  Row332 Row1Row3 3c2d=0 d1.1p=0 2.333d+p=31030  Pivot:Row2Row3 3c2d=0 2.333d+p=31030 d1.1p=0  Row32.333333331 Row2Row3 3c2d=0 2.333d+p=31030 1.529p=13298.571  p=1.5285714313298.57142857=8700 d=2.3333333331030p=2.33333333310308700=9570 c=30+2d=30+2 9570=6380  c=6380 d=9570 p=8700

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Showing 2 comments:
Math student
Let x be the price of a man’s bike, y be the price of a woman’s bike, and z be the price of a child’s bike. Then, we can write the following equations:

y = 1.1x (women’s bikes are 10% more expensive than men’s)

z = 0.67y (children’s bikes are a third cheaper than women’s)

2z + x + y = 31030 (the family paid a total of CZK 31,030 for two children’s, one man’s, and one woman’s bike)

To solve this system, we can use the method of elimination12 or the Wolfram|Alpha calculator1. The solution is:

x = 9000 (the price of a man’s bike)

y = 9900 (the price of a woman’s bike)

z = 6615 (the price of a child’s bike)

2/3 is not 0.67 .... so

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