At a concession stand, popcorn costs $1.10 and nachos cost $2.35. One day, the receipts for a total of 172 popcorn and nachos were $294.20. How many popcorns were sold.

Question

At a concession stand, popcorn costs $1.10 and nachos cost $2.35. One day, the receipts for a total of 172 popcorn and nachos were $294.20. How many popcorns were sold.

Please show work!

I don't understand

Answer 1

let number of nachos be x

then number of popcorns = 172-x

1.1x + 2.35(172-x) = 294.20
times 100
110x + 235(172-x) =29420
110x + 40420 - 235x = 29420
-125x = -10000
x = 88

so 88 nachos and 172-88 or 84 popcorn

Answer 2

To solve this problem, we can set up a system of equations. Let x be the number of popcorns sold and y be the number of nachos sold.

From the given information, we know that:
1) The cost of one popcorn is $1.10, so the cost of x popcorns is 1.10x.
2) The cost of one nacho is $2.35, so the cost of y nachos is 2.35y.
3) The total number of popcorns and nachos sold is 172, so x + y = 172.
4) The total sales from popcorns and nachos is $294.20, so 1.10x + 2.35y = 294.20.

We can now solve the system of equations:
From equation 3) x + y = 172, we can express y in terms of x: y = 172 - x.
Plugging this into equation 4), we get: 1.10x + 2.35(172 - x) = 294.20.
Simplifying the equation: 1.10x + 402.2 - 2.35x = 294.20.
Combining like terms: -1.25x = -107.
Dividing both sides by -1.25: x = 85.6.

Since we can't have a fraction of a popcorn sold, we can round the solution to the closest whole number. Therefore, approximately 86 popcorns were sold.

Answer 3

To solve this problem, we can set up a system of two equations based on the given information.

Let's assume the number of popcorns sold as "p" and the number of nachos sold as "n".

From the given information, we can form the following equations:

1.10p + 2.35n = 294.20 (equation 1) (Total cost of popcorns and nachos)

p + n = 172 (equation 2) (Total number of popcorns and nachos sold)

Now, we can use the method of substitution or elimination to solve these equations and find the value of "p" (the number of popcorns sold).

Let's use the substitution method:

Rearrange equation 2 to get n = 172 - p.

Now, substitute n = 172 - p into equation 1:

1.10p + 2.35(172 - p) = 294.20

Simplify the equation:

1.10p + 403.20 - 2.35p = 294.20

Combine like terms:

-1.25p + 403.20 = 294.20

Subtract 403.20 from both sides:

-1.25p = -109

Divide by -1.25 to solve for p:

p = -109 / -1.25

p = 87.2

We found that the number of popcorns sold is 87.2. However, since it is not possible to sell a fraction of popcorn, we round this down to the nearest whole number.

Therefore, the number of popcorns sold is 87.