# 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:

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**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)

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)

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