Question

Mr. Krabs is keeping a close eye on his income throughout the day. He noticed that after selling 5 Krabby Patties he had $62 in the register. Later on, after selling his 14th Krabby Patty of the day he had $98. Create a linear function and use it to determine how much money was in the register at the beginning of the day.

1.) f(x) = __x+__

2.) How much money was in the register at the beginning of the day?
a.) $43.50
b.) $39.50
c.) $37.00
d.) $42.00

Answer 1

Explanation:

f(x) = ax + b

f(5) = 62 => 5a+b = 62

f(14) =98 => 14a+b= 98

________-

-9a = -36

a = -36/-9 = 4

5a + b = 62

5(4) +b=62

20+b = 62

b = 62-20

b = 42

1) f(x) = 4x + 42

2) the money was in the register at the beginning of the day = $42.00 (option d)

Answer 2

Explanation:

Step 1: Determine the slope or rate of change

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

`m=(98-62)/(14-5)`

`m=(36)/(9)`

`m=4`

This means that they get $4 per Krabby Patty that they sell

Step 2: Determine how much money was in the beginning of the day

`\$62 - (5 * \$4)`

`\$62 - \$20`

`\$42`

Step 3: Create a equation

`f(x) = slope * x + initial\ money`

`f(x) = 4x + 42`

Answer part (1) →
`f(x) = 4x + 42`

Answer part (2) → Option D,
`\$42`