Summer camp options

Question

Summer Camp Options Power Camp charges a flat fee of $30 for a jersey, $55.50 per week for conditioning/drills/lessons, and $20 per week for game fees. All Star Camp charges a flat fee of $20 for a jersey, $46.50 per week for conditioning/drills/lessons, and $34 per week for game fees. Top of Your Game Camp charges a flat fee of $15 for a jersey, $58.25 per week for conditioning /drills/lessons, and $22.25 per week for game fees. Choose a variable to represent the number of weeks to attend camp: Using the variable chose, write an expression for each camp, given its description. Power Camp: All Slar Camp: Top of Your Game Camp:You attended Power Camp and paid $407.50. How many weeks did you spend at Power Camp? Justify your answer (write and solve an equation using the expression you found on slide 1). You attended All Star Camp and paid $342. How many weeks did you spend at All Star Camp? Justify your answer (write and solve an equation using the expression you found on slide 1). You attended Top of Your Game Camp and paid $578.50. How many weeks did you spend at Top of Your Game Camp? Justify your answer (write and solve an equation using the expression you found on slide 1). Afler how many weeks will the cost of Power Camp be the same as the cost of All Star Camp Write and solve an equation to justify your answer. How much will it cost for either campAfter how many weeks will the cost of Power Camp be the same as the cost of Top of Your Game Camp? Write and solve an equation to justify your answer. How much will it cost for either camp? After how many weeks will the cost of All Star Camp be the same as the cost of Top of Your Game Camp? Write and solve an equation to justify your answer. How much will it cost for either camp? If you only want to attend one camp for 3 weeks, which camp would you choose? Explain your reasoning.-

Answer 1

Since we are talking about number of weeks we will let weeks be represented by w.

Anything that is a flat fee is an additional cost to the weekly rate.

Power Camp: $55.50 per week for conditioning/drills/lessons + $20 per week for game fees + $30 for a jersey

Power Camp: 55.50w + 20w + 30

All Star Camp: 46.50w + 34w + 20 s

Top of Your Game Camp: 58.25w + 22.25w + 15

Because they give you a total payment for each camp you can set that equal to the expressions above.

PC: 55.50w + 20w + 30 = $407.50

Combine like terms - 55.50 + 20 = 75.50

75.50w + 30 = 407.50

-- 30 -- 30

------------------------------------

75.50w = 377.50

---------- --------

75.50 75.50

w = 5

Therefore you get 5 weeks with $407.50.

YOu would do the same process for the remaining camps.

In choosing a camp to attend if you only went for three weeks, you would be looking for the better buy.

Enter 3 in for the numbers of weeks into each of the expressions. The cheapest price is the camp you would want to choose.

Ex: PC -- 55.50 (3) + 20 (3) + 30 = total cost

166.50 + 60 = 30 = 256.50

So it would cost $256.50 for 3 weeks at power camp. Now see how much it is for the other camps. Remember to pick the cheapest cost as the better buy.