What is the formula? mathemtics?!?!?

Question

so this is a table:

No. of people (p) 1 2 3 4 5 6 7
Cost of a Holiday (c) £145 £200 £255 ........ ......... ......... ........
formula c= ...... x P + ........

Complete the tables and find a formula conneting the two letters.

No. of Teachers (T) 3 4 5 6 7 8
No. of Pupils (p) 13 18 23 ..... ..... .....

p = .... x t + .....

No. of Trees (t) 4 5 6 7 8 9
No. of bannanas (b) 30 50 70 ..... ..... .....
b= ..... x t +/-

Answer 1

No. of people (p) 1 2 3 4 5 6 7
Cost of a Holiday (c) £145 £200 £255 ........
formula c= 55 P + 90

Complete the tables and find a formula conneting the two letters.

No. of Teachers (T) 3 4 5 6 7 8
No. of Pupils (p) 13 18 23 ..... ..... .....

p = 5 T - 2

No. of Trees (t) 4 5 6 7 8 9
No. of bannanas (b) 30 50 70 ..... ..... .....
b= 20 t - 50

Bye bye and good luck !!

Answer 2

In all 3 problems, you are dealing with a linear function. This becomes clear if you were to plot the points on graph paper and join the points. Be sure to extend the line in both directions beyond the given points.
Problem No.1:
The ordered pairs to plot are
(1,145), (2 200), (3, 355),..... The price is increasing by
55 per person, so the missing four terms are (4,410),
(5,465), (6,520), (7,575)

Now we know that for any straight line, y=mx+b, where m is the slope of the line and b is the y-intercept. That's where the line cuts the y-axis.
For your problem, y is the cost of a holiday and x is the no. of people. In other words, (x,y) =(P,c)
Your equation thus starts to take shape as
c= mP+b
What is m? It's the SLOPE, symbolized as m, and is defined as RISE/RUN, or change in vertical height
divided by change in horizontal distance, between any pair of two given points.
For your problem, let's pick the points (3,255) and
(1,145). The value of m is (255-145)/(3-1)=110/2=55
Your equation now looks like this: c=55P +b
All we need now is b. There are 2 ways to find it.
If you drew the graph, you can see that the y-intercept is 90. That's where the line cuts the y-axis, and it is b.
The second way to find b is to calculate it. Since any
one of the ordered pairs lie on the line, their values must satisfy the equation of the line. I shall pick
(4,310), Plug in 4for P, 310 for c, to get a value for b
310=4(55)+b, from which b=90.
We are done. Our required formula is c=55P+90

Your other problems are done in exactly the same manner. I shall be brief.
Problem No.2
Table is completed with (6,28),(7,33)(8,38). Increases by 5 for an additional teacher.
Slope "m" is (38-28)/(8-6)=10/2=5
p=5t +/- y-intercept b
38=5(8)+b
b=-2
Formula is p=5t-2

Problem No.3
(7,90), (8,110), (9,130)
m=(130-110)/(9-8)=20
b=20t+ B (i used a capital B because formula already uses the small b)
90=20(7)+B, B=-50
b=20t-50

We're done! Glad I could help you.

Answer 3

c = 90 + 55*p

p = (T - 2)*5, T >= 3

b = 10 +(t - 3)*20, t >= 4

Answer 4

1.) c=55P +90

2.) p=5T -2

3.) b=20t -50