At a certain store all radios are equally priced and all tape recorder

Question

At a certain store all radios are equally priced and all tape recorders are equally priced. What price does the store charge for a radio?

(1) The total price of 7 tape recorders is $225 more than the cost of 5 radios.
(2) The total price of 8 tape recorders is $100 more than the price of two radios.

Kudos for a correct  solution .

Skywalker18 · Answer

Let price of a radio = R
price of a tape recorder = T
We need to find R

1. 7T = 225 + 5R
Not sufficient

2. 8T= 100 + 2R
Not sufficient

1-2 , we get
-T= 125 + 3R
=>3R = -T -125
We will get negative value for R .
Answer E
Also,we can multiply equation 1 by 8 and equation 2 by 7 and equate them.
56T = 1800 + 40R

56T = 700 + 14R

1800 +40R = 700 + 14R
=>26R = -1100
=> R = - 42.3

Answer E

mvictor · Answer

agree with the above mentioned explanation. This one is trying to trick you to consider that by having 2 systems of equations, one can solve for individual values. But it is not the case, since we get to negative values, and, unless these are very very bad radios for which the seller needs to pay the customer so that to get rid of them :D, such is not possible.

rhine29388 · Answer

Why is the solution saying C? Even after solving the 2 equations we are getting negative values for price for a radio as - 42.3. How can the price of radio come out to be a negative value unless these are very very bad radios for which the seller needs to pay the customer so that to get rid of them .
there is some sort of information missing from the question stem or the statements without which we can't get the correct solution

At a certain store all radios are equally priced and all tape recorder

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