Question

Terrence is folding paper cranes at a constant rate. The table below shows the amount of time he needs to fold cranes.


Write an equation to describe the relationship between c, the number of cranes, and t, the total time in minutes.

Answer 1

Answer: t = 3.5c

Step-by-step explanation:

1) We know, cranes are folded at constant rate.

So, no. of cranes and time taken must be linearly dependent .

=> All 3 points must form a line .

2) Let us take any two points A (5,17.5)& B(8,28).

Equation of line :

$(t-t_1)=\frac{(t_2-t_1)}{(c_2-c_1)}(c-c_1)\\ \\(t-17.5)=\frac{(28-17.5)}{(8-5)}(c-5)\\ \\=>(t-17.5)=\frac{10.5}{3}(c-5)\\ \\=>(t-17.5)=3.5(c-5)\\ \\=>t=3.5c$

We can cross check, whether third point satisfies this or not,

t = 3.5 * 12=42.

yes, time is 42 minutes for no. of cranes 12 folded.

Hence, Our required relation between t and c is

$\boxed{t=3.5c}$