math problem

[dcowboys107]

Three friends have a tradition of buying each other a New Year’s gift each year. Each person is bought a gift by the other two friends who split the cost equally. Therefore, friend A and friend B each pay half the cost of the gift for friend C, friend B and friend C each pay half the cost of the gift for friend A, and friend C and friend A pay half the cost of the gift for friend B. The final rule for this gift giving process is that the gifts are purchased together on the same day where each person spends all the money they bring to the event.



If friend A brings $50, friend B brings $58, and friend C brings $62, what are the prices for each of the three gifts?

 

[mad_mathematician]

Three friends have a tradition of buying each other a New Year’s gift each year. Each person is bought a gift by the other two friends who split the cost equally. Therefore, friend A and friend B each pay half the cost of the gift for friend C, friend B and friend C each pay half the cost of the gift for friend A, and friend C and friend A pay half the cost of the gift for friend B. The final rule for this gift giving process is that the gifts are purchased together on the same day where each person spends all the money they bring to the event.



If friend A brings $50, friend B brings $58, and friend C brings $62, what are the prices for each of the three gifts?

A = gift for A, B = gift for B, C = gift for C

B+C = 50
A + C = 58
A + B = 62

A-B=8 therefore A=(62+8)/2 = 35, therefore B = 62-35= 27
C=58-A = 58-35 = 23

you just have to be able to form the simultaneous equations, then its easy