Answer:
Sergio will buy the kayak first in 33.33 weeks.
Step-by-step explanation:
Sergio's per week savings = $24
Let the period of the savings = x
Then total savings of Sergio in x weeks = $24x
If y represents the total amount,
y = 24x ------(1)
Table given in the picture represents the savings of Lia.
If the points given in the table are plotted on graph, a straight line is formed.
Let the equation of the line is,
y = mx + b
m = Slope of line
b = y-intercept
Slope of the line = Savings per week
= [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
For two points (4, 72) and (8, 144) lying on the straight line,
Slope 'm' = [tex]\frac{144-72}{8-4}[/tex]
= [tex]\frac{72}{4}[/tex]
= 18
Equation of the line will be,
y = 18x + b
Since, (12, 216) also lies on the line,
216 = 18(12) + b
b = 216 - 216
b = 0
Therefore, equation of the line will be,
y = 18x -----(2)
Cost of kayak = $800
For Lia's savings,
800 = 18x
18x = 800
x = 44.44 weeks
For Sergio,
800 = 24x
x = 33.33 weeks
Therefore, Sergio will be able to buy the kayak first and it will take 33.33 weeks to purchase.
