Solving Linear Equations?

Question

1) You are ordering t-shirts from online which cost $7.00 each. Your shipping cost is $4.50 and your purchase total is $25.50. Let t be the number of t-shirts ordered. Which equation models this situation?

2) How many t-shirts were ordered in question #1?

3) Solve the equation 4 - 2(x - 7) = -12 for x.

4) Solve the equation 3(2x + 1) = 2x - 9 for x

5) One-on-One Gym charges $50 initiation fee and $30 per month. Really-Fit Gym charges $75 initiation fee and $25 per month. For what number of months (m) is the cost the same using the equation 50+30m = 75+25m?

Answer 1

1) Your models is

P = 7*X + 4,5

where P is the purchase total and X is the number of t-shirts

2) by solving the above equation for X and if P=25,5 then X = 3 which is the number of t-shirts ordered in question #1

3) x = 15

4) x = -3

5) for 5 months

Answer 2

This question is 5 different problems:
First, you must answer question 1:
7t+4.50=25.50
now solve for t:
25.50-4.50=7t (move all constants to one side and subtract)
21=7t (now divide to have only the variable)
3=t (you purchased 3 t-shirts)

You now have an answer to question 2:
3 t-shirts

Now let's answer questions 3 and 4:
(simple algebra)
#3:
4-2(x-7)=-12 (now multiply everything)
4-2x+14=-12 (now move all the variables to one side and constants to the other)
4+14+12=2x (do your addition)
30=2x (now divide by 2 to sove for x)
15=x

#4: (use the same rules as question #3)
3(2x+1)=2x-9
6x+3=2x-9
6x-2x= -9-3
4x= -12
x= -3

For question #5, your professor has done the analytical thought and given you the equation to solve for the number of months (m) ~ just solve the equation like any other algebr problem. Follow the algebra rules from above.

50+30m=75+25m
30m-25m=75-50
5m=25
m=5
~ it takes five months to have the two gyms costs the same

I hope this has been helpful!
Jeff

Answer 3

1. 7.00t+4.50=25.50

2. 7t+4.50=25.50
7t=21
t=3

3. 4-2x+14=-12
18-2x=-12
-2x=-30
x=15

4. 6x+3=2x-9
4x= -12
x= -3

5. 50+30m=75+25m
5m=25
m=5

Answer 4

1)
I believe this is how you would set the problem up:
7t+4.50=25.50

2)This is how to get the answer for this problem:
7t+4.50-4.50=25.50-4.50
7t=21
t=3

3 t-shirts were ordered for that amount.

3)
4-2(x-7)=-12
Use distributive property:
4-2x+14=-12
-2x+18=-12
-2x=-30
x=15

Check:
4-2(15-7)=-12
4-2(8)=-12
4-16=-12
-12=-12

4)
3(2x+1)=2x-9
Use distributive property:
6x+3=2x-9
4x+3=-9
4x=-12
x=-3

Check:
3(2(-3)+1)=2(-3)-9
3(-6+1)=-6-9
3(-5)=-15
-15=-15

5)
50+30m=75+25m
50+5m=75
5m=25
m=5 months

Check:
50+30(5)=75+25(5)
50+150=75+125
200=200

I hope this helps!

Answer 5

1) When buying t amount of shirts at $7.00 each with a flat $4.50 fee for shipping, the equation would be: f(t) = $7.00t+$4.50

2) f(t) = $25.50 = $7.00t + $4.50
$21.00 = $7.00t --- -$4.50
3=t --- /$7.00

3) 4-2x+14=-12 means x = 15

4) 6x+3 = 2x - 9 means x = -3

5) m = 5

Answer 6

1) let t be the number of t-shirts ordered.
7t = cos of x t-shirts
shipping = $4.50
7t+4.50=25.50 (model)
2 ) 7t=25.50-4.50=21
t=3 t-shirts

Answer 7

1. 7t+4.50=25.50

2. 3