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1. Companies often sell products at or below cost in order to draw in and retain customers. Redman Manufacturers is tracking 5 items from last month’s sales. On item #1 they make $15; item #2 loses $4; item #3 makes $9; item #4 loses $6; and item #5 makes $12. Last month’s sales are as follows:
Item #1: 90 units sold
Item #2: 103 units sold
Item #3: 78 units sold
Item #4: 45 units sold
Item #5: 164 units sold
Write, simplify, and, calculate the profit or loss for the month.
Calculations:
Item #1-x
Item #2-y
Item #3-z
Item #4-k
Item #5-m
F=15x-4y+9z-6k+12m= 15*90-4*103+9*78-6*45+12*164=1350-412+702-270+1968=3338
Answer: $3338 profit
2. When principal (P) is invested at a rate of (R) over a period of time (T) in years, simple interest (I) is earned. The simple interest is calculated by multiplying the principal, rate, and time. Write an equation to represent this scenario.
Answer: I=PRT
3. Using the formula above, calculate the interest earned for an investment of $15,000 at a rate of 5% over 10 years.
Calculations:
I=1500*0.05*10= 750
Answer: 750
4. The perimeter of a rectangle is P=2L+2W where L is the length and W is the width. Find the perimeter when L=15 and W=25. Show your work.
Calculations:
P=2L+2W=2*15+2*25=30+50=80
Answer: 80
5. The formula for a triangle is A= 12bh. If the area of a triangle is 36 and the height is 9, what is the base?
Calculations:
A= 12bh.
36=(1/2)*9*b
b=36*2/9
b=72/9=8
Answer: 8
6. The formula F= 95C+32 relates Celsius and Fahrenheit temperature. If the current temperature is -20°C, what is the temperature in Fahrenheit?
Calculations:
F= 95C+32
F=95(-20)+32=-9*4+32=-36+32=-4
Answer: -4
7. A triangle has sides measuring x+7, 2x+3, and 5x-6. Write and simplify an expression that represents the perimeter of the triangle.
Calculations:
P= x+7+ 2x+3+ 5x-6= 8x+4
Answer: 8x+4
8. Floral Solutions is calculating their profits for the previous month. Profit is determined by revenue minus the cost. The cost of producing floral arrangements is represented by the equation C= 18+35x and the revenue is represented by the equation R=80x+12.
a. Find the simplified expression that represents the profit.
b. Find the profit made when 110 arrangements are sold.
Calculations:
- P=R-C
P=80x+12-18-35x
P=45x-6
- x=110
P=45*110-6=4950-6=4944
Answer: The expression is: P=45x-6The profit made is: 4944
9. Jamie sold her house for x dollars. The real estate agent received a 5% commission and Jamie received $197,125. Write and solve an equation to determine the selling price of the house.
Calculations:
197.125/95=x/100
X=197.125/0.95=207.5
Answer: 207.5
10. Dan works on commission and earns 4% on all of his sales. In month 1, he sold $25,000; month 2 was $17,000; and month 3 was $34,000. 18% of his total earnings are taken out for taxes. Calculate the total net (after taxes) pay Dan earned over the 3 months. Write and simplify an expression that represents this scenario.
Calculations:
Month 1: 0.04*25000
Month 2: 0.04*17000
Month 3: 0.04*34000
In total: 0.04*25000 + 0.04*17000 + 0.04*34000 = 0.04(25000 + 17000 + 34000) = 3040
18% tax is: 3040*0.18 = 547.2
Net with taxes paid: 3040 - 547.2 = 2,492.8
0.04(25000 + 17000 + 34000)(1 - 0.18) = 2,492.8
Answer: The expression is: 0.04(25000 + 17000 + 34000)(1 - 0.18)
The simplified expression is: 2,492.8
