HELP ME ON THIS MATH PROBLEM AND I'LL GIVE YOU 10 POINTS please?

Question

Five tapes cost as much as two CD'S at the Tape and CD exchange. Carla bought four tapes andd two Cd's for 27 dollars. How much does a CD cost?



Can you please explain how you would work this problem out?
and type out all of your work so I can understand it?
And what is an appropiate equation for this problem?

Answer 1

5T = 2CD
So, 4T + 2CD = 4T + 5T = 9T, by using the first line and substituting the 2CD away
Since $27 = the total cost, and the total cost you found in line two is 9T,
9T = $27
1T = $3
But since in line one 5T = 2CD
5T = 5 times $3 = $15
So $15 = 2CD
2CD = $15
1CD = $7.5

Answer 2

5 tapes= 2 CD
4 tapes+2CD=27$
4 tapes+5 tapes=27$
9 tapes=27$
1 tape=3$
2 C.D= 5 tapes=5*3$=15$
1 CD costs 7.5$

Answer 3

Piece of cake. This is a simple example of two equations in two unknowns. Write down the information you have as two equations (t=tapes, c=CDs). First "Five tapes cost as much as two CD'S " translates to 5t=2c. Next "four tapes andd two Cd's for 27 dollars" translates to 4t+2c=27. Now substitute to get down to one variable: from the first equation you know that 5t and 2c are equivalent, so substitute 5t for 2c and rewrite the second equation as 4t+5t=27. That condenses down to 9t=27, divide by 9 on both sides and you get t=3. Stick 3 back in for t in the first equation and get 5(3)=2c, or 15=2c or c=7.5 and there you have it: t=3, c=7.5, so Tapes are $3 and CDs are $7.50. plug the numbers back into the second equation to check that the results are correct: 4(3)+2(7.5)=27? Yes it does. Now go do the rest of your homework!

Answer 4

okay i suck at algebra but here it goes. let x = the 2 cd's
so a tape is 1/5 x

x + 4/5x = 27 multiply everything by 5 to get rid of the fraction

5x + 4x = 135 combine like terms

9x = 135 divide by 9

x = 15 you are looking for the price of one cd so divide the answer by 2

1/2 x = 7.5 so one cd is $ 7.50!


and I notice that everyone else used 2 variables but it is much simpler to use ne and think of the other in terms of the first variable!

Answer 5

the easiest way to do this problem is to set

the tapes equal to a variable-lets choose x
the cd's equal to another variable-lets choose y

the given information is that

5x = 2y, that is, 5 tapes are equal in cost to 2 cd's and
4x + 2y = 27, that is, 4 tapes and and 2 cds cost 27

now, you solve for y in the first equation and you get
5x = 2y
5x/2 = y

now that you know what y is equal to in terms of x, substute in the value for y in the second equation

4x + 2(5x/2) = 27 now solve for x in this equation
4x + 10x/2 = 27
4x + 5x = 27
9x = 27
x=3

now you know the cost of the tapes is $3.00

now substitute this back into either equation to get the value of y

5(3) = 2y
15 = 2y
7.50 = y

double check with the other equation

4(3) +2y = 27
12 + 2y = 27
2y = 15
y=7.50

the cost of the cd's is $7.50

Answer 6

the easiest way to do this problem is to set

the tapes equal to a variable-lets choose x
the cd's equal to another variable-lets choose y

the given information is that

5x = 2y, that is, 5 tapes are equal in cost to 2 cd's and
4x + 2y = 27, that is, 4 tapes and and 2 cds cost 27

now, you solve for y in the first equation and you get
5x = 2y
5x/2 = y

now that you know what y is equal to in terms of x, substute in the value for y in the second equation

4x + 2(5x/2) = 27 now solve for x in this equation
4x + 10x/2 = 27
4x + 5x = 27
9x = 27
x=3

now you know the cost of the tapes is $3.00

now substitute this back into either equation to get the value of y

5(3) = 2y
15 = 2y
7.50 = y

double check with the other equation

4(3) +2y = 27
12 + 2y = 27
2y = 15
y=7.50

the cost of the cd's is $7.50

Answer 7

You have two variables so you need two equations to solve it:

5 * T = 2 * C

4 * T + 2 * C = 27

From the first equation : T = (2 * C)/5

now plug this value for T back into the 2nd equation and get:

4 * (2 * C)/5 + 2 * C = 27
then you get
8C/5 + 2C = 27 ==> 18/5C=27 or
C = 27 divided by 3 3/5

now that you know what C is go back and plug into the first (simpler) equation to solve for T.

Isn't that simple?

Answer 8

lets say a price of a tape is x,and price of a CD is y. so first equation we have is 5x=2y.and the second one is 4x + 2y =27.(the ones Carla bought)Now, all we gotta do is to solve both equations.as follows,

as you can see in the first equation 5x is equal to 2y.Thus, we can replace 2y in the second equation as 5x.(and the new equation will be 4x + 5x= 27, and 9x is 27.so x is 3, which was the price of a tape.)
now we can turn back to the first equation(5x=2y)now, if we again replace x as 3 in this eq.,we will get (5 times 3 = 2y)which means 15 =2y.and y is 7,5(which gives us the price of a CD.)

Answer 9

T= cost of tape
C=cost of CD

then
5*T=2*C
and
4*T+2*C=27

so

4*T+5*T=27 => T=3 and C=7.5

Answer 10

Let T = the price of a tape
Let C = the price of a CD

Now 5T = 2C this is the first equation
From this T = (2/5)C or T = 0.4C

The second equation is 4T + 2C = 27
Sub in the first equation into the second
4 * (0.4C) + 2C = 27
3.6C = 27
C = 27/3.6 = 7.5 dollars is the price of the CD
and T = 0.4 * 7.5 = 3 dollars is the price of the Tape

Cheers

Answer 11

work out how much the tapes cost and then see how much the CD's cost i hate those math problem i get them on the star9 all the freakin time but i think the tapes cost 5 or less but take my math advice seriously i suck at math too! i just kind of get these problems tho they want to divide