Two records and three tapes cost $31. Three records and two tapes cost $29. Find the cost of each records and each tape.
2R + 3T=31
3R+2T=29
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Two equations and two unknowns. Solve the two equations simultaneously. Post your work if you get stuck.
is my answer correct?
T = 7
R = 5
?
Yes, but you could check it.
(2*5)+(3*7)= 10 + 21 = 31 AND
(3*5)+(2*7) = 15+14=29 so both equations check.
To solve this problem, we can set up a system of equations based on the given information.
Let's assume the cost of one record is "x" dollars and the cost of one tape is "y" dollars.
According to the first statement, two records and three tapes cost $31:
2x + 3y = 31 -- Equation 1
According to the second statement, three records and two tapes cost $29:
3x + 2y = 29 -- Equation 2
To solve this system of equations, we can use the method of substitution or elimination.
Let's use the method of elimination to eliminate the variable "x".
Multiply Equation 1 by 3 and multiply Equation 2 by 2 to make the coefficients of "x" the same:
(3)(2x + 3y) = (3)(31)
(2)(3x + 2y) = (2)(29)
Simplifying these equations, we get:
6x + 9y = 93 -- Equation 3
6x + 4y = 58 -- Equation 4
Now, we can subtract Equation 4 from Equation 3 to eliminate "x".
(6x + 9y) - (6x + 4y) = 93 - 58
6x - 6x + 9y - 4y = 35
5y = 35
Simplifying, we find that y = 7.
Now, substitute y = 7 into either Equation 1 or Equation 2 to find the value of x.
Let's use Equation 1:
2x + 3(7) = 31
2x + 21 = 31
2x = 31 - 21
2x = 10
x = 5
Therefore, the cost of one record is $5, and the cost of one tape is $7.