Question

Please help me with this question

Answer 1

Sergio will buy the kayak first in 33.33 weeks.

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

=
`(y_2-y_1)/(x_2-x_1)`

For two points (4, 72) and (8, 144) lying on the straight line,

Slope 'm' =
`(144-72)/(8-4)`

=
`(72)/(4)`

= 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.