One day, a deli sold a total of 39 hamburgers and hot dogs. The revenue from these sales was $137.35. The hamburgers were $3.87 each and the hot dogs cost $2.90 each.
a) Write a mathematical expression for the number of burgers, x, and the number of hot dogs, y, sold that day.
Answer:
b) Write a mathematical expression for the amount of revenue from this day's sales. Use x for the number of burgers and y for the number of hot dogs.
Answer:
c) How many hot dogs did the store sell that day? (Include the word hot dogs in your answer).
Answer:
x = 39 - y
3.87x + 2.90y = 137.35
Substitute 39-y for x in the second equation and solve for y. Insert that value into the first equation to solve for x. Check by putting both values into the second equation.
a) Since the total number of hamburgers and hot dogs sold is 39, we can write the mathematical expression as:
x + y = 39
b) The revenue from the sales can be calculated by multiplying the number of hamburgers (x) by the price per hamburger ($3.87) and the number of hot dogs (y) by the price per hot dog ($2.90). So the mathematical expression for the revenue is:
Revenue = (3.87 * x) + (2.90 * y)
c) To find the number of hot dogs sold that day, we can substitute the value of x from the first equation into the second equation:
x + y = 39
y = 39 - x
Now we can substitute this value of y into the revenue equation:
Revenue = (3.87 * x) + (2.90 * (39 - x))
To answer this question, we don't actually need to solve the equation, but it can be simplified as:
Revenue = (3.87 * x) + (2.90 * 39) - (2.90 * x)
Revenue = 3.87x + 113.1 - 2.90x
Revenue = 0.97x + 113.1
So, the mathematical expression for the amount of revenue from this day's sales is Revenue = 0.97x + 113.1.
To determine the number of hot dogs, we need to know the value of x (the number of hamburgers sold).
a) Mathematical expression for the number of burgers, x, and the number of hot dogs, y, sold that day:
x + y = 39
b) Mathematical expression for the amount of revenue from this day's sales, using x for the number of burgers and y for the number of hot dogs:
3.87x + 2.90y = 137.35
c) The number of hot dogs the store sold that day:
Let's solve the two equations simultaneously to find the values of x and y.
From equation 1:
x + y = 39
Solving for x:
x = 39 - y
Substituting this value of x into equation 2:
3.87(39 - y) + 2.90y = 137.35
Expanding and simplifying:
151.53 - 3.87y + 2.90y = 137.35
-0.97y = -14.18
y = 14.18 / 0.97
y ≈ 14.61
Therefore, the store sold approximately 14.61 hot dogs that day.
a) The mathematical expression for the number of burgers, x, and the number of hot dogs, y, sold that day can be written as:
x + y = 39
b) The mathematical expression for the amount of revenue from this day's sales can be written as:
Revenue = (number of burgers * price per burger) + (number of hot dogs * price per hot dog)
Revenue = (x * $3.87) + (y * $2.90)
Revenue = 3.87x + 2.90y
c) To find out how many hot dogs the store sold that day, we need to solve the equations from parts a) and b). From part a), we know that x + y = 39. And from part b), we have the equation Revenue = 3.87x + 2.90y and we know that the revenue was $137.35.
So, we can set up the equation:
137.35 = 3.87x + 2.90y
We can solve this system of equations to find the values of x and y.