Honors Geometry Problem set#2

[Twins]

Please can someone help me with this problem; thank you so much......

Question: 1. The math club is planning a pie day (3.14) pie sale to raise funds for their March 14th field trip to a local road race of length 3.14 miles. The bakery the math club is working with charges $100 for the labor and an extra $5 for each pie. The club plans to sell the pies for $7 each.

a) Write an expression for the math club's total cost for the pies from the bakery.

b) Write an expression for the money taken in by the math club for the pies it sell.

c) What is the break even point for sales?

d) How much profit will it make if it purchases 100 pies, but only sells 90?

e) How much profit will the math club make if it sells 100 pies?

 

[soroban]

Hello, Twins!

The math club is planning a pie sale to raise funds.
The bakery charges $100 for the labor plus $5 for each pie.
The club plans to sell the pies for $7 each.

a) Write an expression for the math club's total cost for the pies from the bakery.

Let \(\displaystyle x\) = number of pies bought from the bakery.

\(\displaystyle Cost \:=\:100\,+\,5x\)

b) Write an expression for the money taken in by the math club for the pies it sell.

Let \(\displaystyle y\) = number of pies sold.

\(\displaystyle Revenue\:=\:7y\)

c) What is the break-even point for sales?

We assume that \(\displaystyle x\,=\,y\)

If \(\displaystyle \,Revenue\:=\:Cost\), we have: \(\displaystyle \,7x\:=\;100\,+\,5x\;\;\Rightarrow\;\;x\,=\,50\)

The math club must buy and sell 50 pies to break even.

d) How much profit will it make if it purchases 100 pies, but only sells 90?

\(\displaystyle Profit\;=\;Revenue\,-\,Cost \;= \;7y\,-\,(100\,+\,5x)\;=\;7y\,-\,5x\,-\,100\)

The club buys 100 pies \(\displaystyle (x\,=\,100)\) and sells 90 \(\displaystyle (y\,=\,90)\).

\(\displaystyle Profit\;=\;7(90)\,-\,5(100)\,-\,100\;=\;\$30\)

e) How much profit will the math club make if it sells 100 pies?

If the club buys 100 pies \(\displaystyle (x\,=\,100)\) and sells 100 pies \(\displaystyle (y\,=\,100)\),

\(\displaystyle \;\;Profit\;=\;7(100) \,-\,5(100)\,-\,100\;=\;\$100\)