Question

Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.

Answer 1

Answer:

First question:  f(x) = 23(1.17)ˣ; Second question:  f(x) = 27(1.13)ˣ; Third question:  f(x) = 13x - 170; Fourth question:  f(x) = 17x + 23

Explanation:

First question:  Shop A sells 11 units and Shop B sells 12 units.  Together, this is 11+12 = 23 units.  The rate of sales is expected to increase by 17%; this means they will sell 100% of the current sales and an extra 17%:

100+17 = 117%; 117% = 117/100 = 1.17

This gives us the equation f(x) = 23(1.17)ˣ

Second question:  We want to find the difference between element A, 44(1.13)ˣ, and element B, 17(1.13)ˣ:

44(1.13ˣ) - 17(1.13ˣ)

Factor out the common factor, 1.13ˣ:

1.13ˣ(44-17) = 1.13ˣ(27) = 27(1.13)ˣ

Third question:  Selling x shirts for $13 each gives us the expression 13x.  She plans to donate $270; this means she would subtract it from her profits, giving us the function

f(x) = 13x-270

Fourth question:  We subtract the length of the patio, 13x+6, from the length of the backyard, 30x+29:

30x+29 - (13x+6) = 30x+29 - 13x - 6

Combine like terms:

30x-13x + 29-6

17x + 23

This gives us the function

f(x) = 17x + 23

Answer 2

1) Jason: Shop A - 11 units; Shop B - 12 units. Sales increase at 17% per week. So, 11 + 12 = 23.
 
f(x) = 23(1.17)ˣ

2) Daniel: Element A temp - 44(1.13)ˣ ; Element B temp - 17(1.13)ˣ. How much temp of Element A be more than the temp of Element B.

f(x) = 44(1.13)ˣ - 17(1.13)ˣ = 27(1.13)ˣ
f(x) = 27(1.13)ˣ

3) Maggie: Tshirt price - $13. Charity donation - 270

f(x) = 13x - 270

4) Mr. Smith: Length of backyard - 30x + 29 ; Length of square patio - 13x + 6
Length not covered by the patio.

f(x) = (30x + 29) - (13x + 6) = 30x - 13x + 29 - 6 = 17x + 23
f(x) = 17x + 23