Joshua asked some surfers how many beaches they had been to in the last month. 100 surfers responded to his survey. His results are shown in the table below.
a) Work out the value of c + d.
b) Joshua calculated that the mean number of beaches that the surfers had been to in the last month was 2.27. Use this information to work out the value of c + 4d.
c) Work out the values of c and d.
Number of beaches
1 2 3 4
Number of surfers
c 24 4 d
To solve the problem step by step, let’s break down each part:
a) Work out the value of c + d.
Since 100 surfers responded, we know:
c + 24 + 4 + d = 100.
This simplifies to:
c + d + 28 = 100.
Therefore:
c + d = 100 – 28 = 72.
b) Use the mean to work out the value of c + 4d.
The mean number of beaches is given as 2.27, which can be calculated by the formula:
Mean = (Total number of responses) / (Total number of surfers)
We can set up the equation:
(1 * c + 2 * 24 + 3 * 4 + 4 * d) / 100 = 2.27.
Calculating the numbers:
c + 48 + 12 + 4d = 2.27 * 100,
c + 4d + 60 = 227,
c + 4d = 227 – 60 = 167.
c) Work out the values of c and d.
Now we have two equations:
1. c + d = 72
2. c + 4d = 167
We can substitute equation 1 into equation 2.
From equation 1, c =