Question

Solve a system of equations using any method: word problems

Answer 1

Using the cost formula, we now know that the cost of each ticket costs $51 and $27.

What is the cost?

• Given a specified quantity of goods produced, a cost function is a mathematical formula that may be used to determine the overall cost of production.
• Below, the cost function will be thoroughly examined.
• A way to show unit expenses in relation to how many units of one or more were generated during a construction project.

We know that so far, they have sold 69 balcony tickets and 48 general admission floor tickets for Friday's show, for a total of $3,828 in receipts.

• For Saturday's show, 91 balcony tickets and 61 general admission floor tickets have been sold, equaling $4,984 in receipts.
• 98×B + 70×G = 6888 ....(1)

If we continue to follow this method, the second equation is:

• 85×B + 30×G = 5145 ....(2)

So let's fix this as follows:

• 98×B + 70×G = 6888
• 85×B + 30×G = 5145

Then,

30×G and 70×G are present.

We obtain this by multiplying the first equation by 3 and the second by 7.

• 3×98×B + 210×G = 3×6888
• 7×85×B + 210×G = 7×5145

Add the second equation and subtract the first.

The terms of G will cancel:

• (3×98 - 7×85)×B
• 3×6888 - 7×5145
• -301 × B = -15351
• B = 51

Let's add B=51 to the initial equation.

• 98×51 + 70×G = 6888
• 4998 + 70×G = 6888
• 70×G = 1890
• G = 27

Therefore, using the cost formula, we now know that the cost of each ticket costs $51 and $27.

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