Algebra - Total Cost of Health Club

Running head: ALGEBRA
ALGEBRA
Name of the Student
Name of the University
Author Note

1ALGEBRA
Solve algebraically.
1.
Energy Cardio offers membership for a fee of $50 plus a monthly
fee of $20.
Exercise Duo offers membership for a fee of $100 plus
a monthly fee $15. After how many months will the total cost of
each health club be the same? What will be the total cost of each
health club?
Solution: Let the month after the cost of each health will become same =
y.
Let the Amount after the ‘y’ months is x.
Hence algebraically,
There will be two equation for two scenarios,
50 + 20y = x ---------(i)
100 + 15y = x ---------(ii)
Solving equations,
 x = 50 + 20y = 100 + 15y
 50 + 20y = 100 + 15y
 20y – 15y = 100 – 50
 5y = 50
 y = 10
hence the month will be 10.
Putting the value of y in equation (i),
 50 + 20*(10) = x
 x = 250 Ans.
2. After a 20% reduction, you buy a tablet for $160. What was the
tablet’s price before the reduction?
Let the tablet’s price before reduction = x.
Hence, According to question,
 x – 20% of x = 160
 x – 20x/100 = 160
 x – x/5 = 160
 (5x-x)/5 = 160
 4x/5 = 160
 4x = 160*5
 x = (160*5)/4

2ALGEBRA
 x = 200 Ans.
Graph on a number line:
3. (-2, 6)
4. Evaluate the function at the given values of the independent
variable and simplify.
F(x)=2x +4
a.
f (-x) b.
f (5) c.
f(x+2)
a. solution:
=> f(-x) = 2(-x) +4
=> f(-x) = 4 -2x Ans.
b. solution:
=> f(5) = 2*5 + 4
=> f(5) = 14 Ans.
c. solution:
=> f(x+2) = 2(x+2) + 4
=> f(x+2) = 2x +4 +4
=> f(x+2) = 2x + 8 Ans.
5. On a piece of graph paper, solve the following system of
equations graphically.
Y=2x +3 ----- (i)
X + y = 0 ------(ii)
Solution:
For equation (i)
Let x = 1