After 11 days
when the number of days was more than 10, the price for the special offer was less than the full price
Step-by-step explanation:
Part D
From the previous information:
The equation for the full price:
y = 7x
The equation for the special offer:
y = 4x + 30
For the special offer to be a better deal, we need to equate both equations above:
y = y
7x = 4x + 30
subtract 4x from both sides:
7x - 4x = 4x - 4x + 30
3x = 0 + 30
3x = 30
divide both sides by 3:
3x/3 = 30/3
x = 10
let's check which days make it better:
we go for a day before 10; 10; and a day after 10
x = 9, 10, 11
for x = 9
y = 7x = 7(9) = 63
y = 4x + 30 = 4(10) + 30 = 70
for x = 10
y = 7(10) = 70
y = 4x + 30 = 4(10) + 30 = 70
for x = 11
y = 7(11) = 77
y = 4(11) + 30 = 74
From the above, when the days is 11 the cost for the special offer is lees than the cost for the full price.
Hence, the special offer will be a better deal on the 11th day
This can be seen graphically when you plot both equation.
The point where they meet will be the point where the cost will be the same for both the special offer and the full price.
This is at point (10, 70).
After this point: when the number of days was more than 10, the price for the special offer was less than the full price.
Thus making it a beter deal.