Help please show steps to solve.
Two records and three tapes cost $31. Three records and two tapes cost $29. Find the cost of each records and each tape.
No examples to guide me.
thanks,
Carol
Make a system.
let r represent records, and t represent tapes.
your system should be:
{2r+3t=$31
{3r+2t=$29
I suggest using elimination.
muliply ALL of the second equation by negative 3.
-3(3r+2t=$29
you'll get:
-9r-6t=-$87
Then multiply the first equation by a positive 2.
2(2r+3t=$31)
you'll get:
4r+6t=$62
Add the two new equations.
4r+6t=62
+ -9r-6t=-87
You should then eliminate the t's, and just get:
-5r=535
divide by -5.
actually wait, that gives you a negative answer......hmmm..........
Maybe you should disregard my work, but i know for a fact that you make a system the way i did. sorry.
To solve this problem, we can use a system of equations.
Let's assume the cost of a record is 'x' dollars and the cost of a tape is 'y' dollars.
From the given information, we can write two equations:
Equation 1: 2x + 3y = 31
Equation 2: 3x + 2y = 29
To solve this system of equations, we can use the method of substitution or elimination. Let's solve it using the elimination method:
Step 1: Multiply Equation 1 by 2 and Equation 2 by 3 to make the coefficients of 'x' in both equations the same:
Equation 1: 4x + 6y = 62
Equation 2: 9x + 6y = 87
Step 2: Subtract Equation 1 from Equation 2 to eliminate 'y':
(9x + 6y) - (4x + 6y) = 87 - 62
5x = 25
x = 5
Step 3: Substitute the value of 'x' into Equation 1 or Equation 2 to find the value of 'y'.
Using Equation 1:
2(5) + 3y = 31
10 + 3y = 31
3y = 31 - 10
3y = 21
y = 7
Therefore, the cost of each record is $5 and the cost of each tape is $7.
I hope this helps! Let me know if you have any further questions.