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3. Luke, the furniture maker, knows that he has 54 stools in stock. Some of these stools have three legs and some have four legs. Luke, however, does not know how many of each type of stool he has in stock. Since the stools are stored upside down, he only counts the number of legs to find out how many of of stool he has in stock. He counts 200 legs. each type 3.1 If the number of four-legged stools is x, write an algebraic expression for the number of three-legged stools. 3.2 Now write algebraic expressions for the number of legs that the three- legged stools have altogether as well as the number of legs that the four- legged stools have altogether. 3.3 Use your answers to Question 3.2 to write an equation in x and then determine the number of four-legged and three-legged stools in stock.​

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adioabiola

The number of number of four-legged and three-legged stools in stock is 38 and 16 respectively.

Simultaneous equation

let

  • number of four-legged stools = x
  • number of three-legged stools = y

x + y = 54

4x + 3y = 200

From equation (1)

x = 54 - y

  • Substitute x = 54 - y into

4x + 3y = 200

4(54 - y) + 3y = 200

216 - 4y + 3y = 200

216 - y = 200

- y = 200 - 216

-y = -16

y = 16

  • substitute y = 16 into

x + y = 54

x + 16 = 54

x = 54 - 16

x = 38

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