Question

Please help

Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.

The student council at Lakewood High School is making T-shirts to sell for a fundraiser, at a price of $11 apiece. The costs, meanwhile, are $10 per shirt, plus a setup fee of $54. Selling a certain number of shirts will allow the student council to cover their costs. What will the costs be? How many shirts must be sold?

Answer 1

The system of equations to describe the situation is:

* $10x + 54 = 11y$

* $y = 11x$

To solve using substitution, we can substitute the second equation into the first equation. This gives us:

* $10x + 54 = 11(11x)$

* $10x + 54 = 121x$

* $-11x = -54$

* $x = 5$

We can then substitute this value of $x$ into the second equation to solve for $y$. This gives us:

* $y = 11(5)$

* $y = 55$

Therefore, the student council will need to sell 55 T-shirts to cover their costs. The costs will be $54 + $10(55) = $604.

Here is the solution in a table format:

| Variable | Value |

|---|---|

| $x$ | 5 |

| $y$ | 55 |

| Cost | $604 |

I hope this helps!

Explanation: