A local food truck specializes in gourmet grilled cheese sandwiches. Each month, the owners of the truck have a constant total of $7,900 in expenses (salaries, truck loan, etc.) and it costs $1.70 per sandwich to make each sandwich. The food truck sells its sandwiches for $7.75 each.

a) Write an inequality to represent how many sandwiches, s, the food truck will have to sell each month to earn more money from selling sandwiches than it pays in expenses and sandwich costs.

b) Solve the inequality. Show your steps or explain your answer.

c) To gain more sales, the food truck offers a discount one month of $1.50 off its sandwiches.

How many more sandwiches will it need to sell to earn more money from selling sandwiches than it pays in expenses and food costs? Explain your answer, mathematically or in words.

a) Therefore, the inequality that represent the number of sandwiches the food truck will have to sell each month to earn more money from selling sandwiches than it pays in expenses and sandwich costs is given as follows;

s × ([tex]c_s[/tex] - [tex]p_s[/tex]) > C

Substituting the known values, gives;

s × ($7.75 - $1.70) > $7,900.00

b) From the inequality, which we have;

s > $7,900/($7.75 - $1.70)

However, $7,900/($7.75 - $1.70) = 158,000/121 ≈ 1,305.79

We round up to the nearest whole number since we are counting sandwiches which are counted per each piece

Therefore;

s > 1,306 sandwiches

An explanation is that the food truck will have to sell more than 1,305 sandwiches to be earn more money than it pays in expenses and sandwich costs.

c) The amount in discount the food truck offers in a specific month = $1.50

Therefore, the amount the food truck sells the sandwich in the given month [tex]c_s[/tex] = $7.75 - $1.50 = $6.25

Therefore the number of sandwich the food truck company will have to sell on that month to earn more money from selling sandwiches than it pays the in expenses and sandwich cost, "s" is given as follows;

s × ([tex]c_s[/tex] - [tex]p_s[/tex]) > C

s × ($6.25 - $1.70) > $7,900, which gives;

s > $7,900/($6.25 - $1.70)

$7,900/($6.25 - $1.70) ≈ 1,73.26

We round up to get, s > 1,737

We round up

Therefore, the number of more (extra) sandwiches the food truck have to sell to earn money from selling sandwiches than it pays in expenses and food costs is the difference in the number of sandwiches it has to sell at $7.75 and $6.25 to earn more money than it pays in fixed expenses (costs) and the sandwich cost which is given as follows;

At $7.75 the number of sandwiches the food truck has to sell s > 1,306

At $1.70 the number of sandwiches the food truck has to sell is s > 1,737

The more number of sandwiches it has to sell = 1,737 - 1,306 = 431 more sandwiches

The more number of sandwiches it has to sell = 431 more sandwiches

(From which we check to have; 1306 + 431 = 1737 which is correct)

psm22415 psm22415 · Answer 2 · 2021-12-23T08:05:56+01:00

The inequality represents how many sandwiches, the food truck is [tex]s \times ($7.75 - $1.70) > $7,900.00[/tex]

The solution of the inequality is,1,305.79

The more number of sandwiches it has to sell is 1373 more sandwiches

Given that,

A local food truck specializes in gourmet grilled cheese sandwiches.

Each month, the owners of the truck have a constant total of $7,900 in expenses (salaries, truck loan, etc.) and it costs $1.70 per sandwich to make each sandwich.

The food truck sells its sandwiches for $7.75 each.

We have to determine,

Write an inequality to represent how many sandwiches, the food truck.

Solve the inequality.

To gain more sales, the food truck offers a discount one month of $1.50 off its sandwiches.

How many more sandwiches will it need to sell to earn more money from selling sandwiches than it pays in expenses and food costs

According to the question,

The constant total expenses (fixed cost), C = $7,900

The cost takes to make each sandwich, = $1.70

The price at which the food truck sells its sandwiches, = $7.75

Where "s" represents the number of sandwiches sold.

The inequality that represents the number of sandwiches the food truck will have to sell each month to earn more money from selling sandwiches than it pays in expenses and sandwich costs is given as follows;

[tex]s \times (c_s-p_s)>c[/tex]

Substituting the known value in the equation,

[tex]s \times ($7.75 - $1.70) > $7,900.00[/tex]

The inequality, which we have; s > $7,900/($7.75 - $1.70)

$7,900/($7.75 - $1.70)

= 158,000/121

≈ 1,305.79

The nearest whole number since we are counting sandwiches which are counted per piece.

Therefore;

s > 1,306 sandwiches

An explanation is that the food truck will have to sell more than 1,305 sandwiches to earn more money than it pays in expenses and sandwich costs.

The amount in discount the food truck offers in a specific month = $1.50 Therefore, the amount the food truck sells the sandwich in the given month = $7.75 - $1.50 = $6.25

The number of sandwiches the food truck company will have to sell on that month to earn more money from selling sandwiches than it pays the in expenses and sandwich cost, "s" is given as follows;

[tex]s \times (c_s-p_s)>c[/tex]

s × ($6.25 - $1.70) > $7,900, which gives;

s > $7,900/($6.25 - $1.70)

$7,900/($6.25 - $1.70) ≈ 1,73.26

s > 1,737

Therefore, the number of more (extra) sandwiches the food truck have to sell to earn money from selling sandwiches than it pays in expenses and food costs is the difference in the number of sandwiches it has to sell at $7.75 and $6.25 to earn more money than it pays in fixed expenses (costs) and the sandwich cost which is given as follows;

At $7.75 the number of sandwiches the food truck has to sell s > 1,306

At $1.70 the number of sandwiches the food truck has to sell is s > 1,737

The more number of sandwiches it has to sell = 1,737 - 1,306 = 431 more sandwiches

The more number of sandwiches it has to sell = 431 more sandwiches

= 1306 + 431 = 1737

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