As a way of saying, “Thank You.”, Katie wants to use her birthday money to send masks to the staff at the nursing home where her grandmother lives. She has two options to do this.
Option 1: Make them herself:
Katie came up with an equation to represent her total cost (including sending them).
y = 4.95 x + 18
+
Option 2: Order online from a company that charges a fixed shipping fee:
Option 2 equation:
No. of masks ordered
Total Cost
10
71.50
20
119.00
30
166.50
Which option costs less per mask?
If she has $142 to spend total, which option should she choose?
How many masks will she be able to send?
two straight lines
first one you say is y = 4.95 x + 18
second one
slope = m = (119-71.5)/10 which is luckily (166.5 - 119)/10 = 4.75
so
y = 4.75 x + b
fund b
119 = 4.75 (20) + b
b = 119 - 95 = 24
so
y = 4.75 x + 24
where do the lies cross?
y = 4.95 x + 18 (cheaper if x small)
y = 4.75 x + 24 (cheaper if x big)
to solve for x where cost is the same
subtract
0 = 0.20 x - 6
so
x = 6/0.2 = 30 then y = 4.75(30) + 24 = $166.50
now we have $142,so fewer than crossing point so use
y = 4.95 x + 18
142 = 4.95 x + 18
4.95 x = 124
x = 25 masks