Question

Each chair that is added to this stack makes it 8cm taller. One chair is 55cm tall. Use your knowledge of patterns to find how high a stack of chairs will be that has 8 chairs in it. 1.5.1 Write down the constant difference 1.5.2 Using the general rule, determine how many chairs would there be if the stack was 127cm high?​

Answer 1

1.5.1 : constant difference is 8

1.5.2: When there are 10 chairs stacked, it's 127 cm tall.

Explanation:

There is a linear relationship between the height of the stack and the number of chairs.

1 chair = 55 cm + 0 extra cm = 55cm

2 chairs = 55cm + 8cm = 63 cm

3 chairs = 55cm + 8(2)cm = 71 cm

4 chairs = 55cm + 8(3)cm = 79 cm

1.5.1 the constant difference between all the underlined numbers above is 8.

1.5.2 You could just keep calculating above until you get 127 cm. (Your teacher might not like that, but it's an option!)

You can find the equation & either solve for the number of chairs OR graph it.

So if we let C = the number of stacked chairs, our equation for H (height) would be:

H = 55 + 8(C-1)

If we substitute H = 127, solve for C.

127 = 55+ 8(c-1)

127 = 55+ 8c-8

127 = 47 + 8c

127 -47 = 8c

80 = 8c

10=c

When there are 10 chairs stacked, it's 127 cm tall.

Check that the answer works:

55 cm (1st chair) + 8*9 (8cm for each additional chair) = 55+ 72 = 127 cm