Answer: 600 of the 500ml energy drinks be sold be sold at $45
Explanation:
The linear relationship between the price (p) of 500ml soft drink and the number sold (x) is expressed as
x = ap + b
At N$20 she sells 1500 of the 500ml soft drinks. This means that the first equation would be
1500 = 20a + b - - - - - - - - -1
the quantity sold falls by 200 of the 500ml soft drinks when she increases the price by 50%. This means that the new quantity sold is 1500 - 200 = 1300
The price at which they were sold is
20 + (50/100 × 20) = $30
The second equation would be
1300 = 30a + b - - - - - - - - -2
Subtracting equation 2 from equation 1, it becomes
200 = - 10a
a = 200/- 10 = - 20
Substituting a = - 20 into equation 2, it becomes
1300 = 10 × - 20 + b
1300 = - 200 + b
b = 1300 + 200 = 1500
The linear relationship becomes
x = - 20p + 1500
If x = 600, then
600 = - 20p + 1500
- 20p = 600 - 1500 = - 900
p = - 900/ - 20
p = $45