Another algebra 2 question?

Question

a grocery store bought ice cream for $2.40 per half gallon and stored it in two freezers. during the night one freezer malfunctioned and ruined 14 half gallons. If the remaining ice cream is sold for 4.06 per half gallon, how many half gallons did the store buy if they made a profit of $105.84?

so what i want to know is how many half gallons did the store buy if they made a profit of $105.84?

Answer 1

No. of half-gallons bought (x):

$4.06(x - 14) - $2.40x = $105.84

$4.06x - $56.84 - $2.40x = $105.84

$1.66x = $162.68

x = 98

Answer: 98 half-gallons were bought.

Proof (profit is $105.84):

= $4.06(98 - 14) - $2.40(98)

= $4.06(84) - $235.20

= $341.04 - $235.20

= $105.84

Answer 2

they bought x number of 1/2 gallons at 2.40 per half gallon.

2.4(x) = cost of all ice cream

4.06(x-14) = $ amount sold

4.06(x-14)- 2.4x =105.84

x = 98 1/2 gallons

Answer 3

let x be the number of half-gallons the store bought

it spent 2.4x on the ice cream

it sold (x - 14) half-gallons at 4.06 (because 14 of the original x were ruined)

4.06(x - 14) - 2.4x = 105.84 (profit)

now solve for x

4.06x - 14(4.06) - 2.4x = 105.84

1.66x = 105.84 + 56.84 = 162.68

x = 162.68 / 1.66 = 98

the store bought 98 half gallons at 2.40 ($235.20 cost)

it sold 84 half gallons at 4.06 ($341.04 income)

341.04 - 235.20 = 105.84 profit