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For a cost of P 100.00, a box of apples was jointly purchased by Maria, Elena and Ana.

For a cost of P 100.00, a box of apples was jointly purchased by Maria, Elena and Ana.

Elementary Algebra
Elementary Algebra
17th Edition
ISBN:9780998625713
Author:Lynn Marecek, MaryAnne Anthony-Smith
Publisher:Lynn Marecek, MaryAnne Anthony-Smith
Chapter3: Math Models
Section3.3: Solve Mixture Applications
Problem 3.66TI: has $8,000 to save for his daughter’s college education. He wants to divide it between one account...
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How did you derive to get these values (encircled)? Please show the complete solution.
For a cost of P 100.00, a box of apples was jointly purchased by Maria, Elena and Ana. One-half of what Maria paid added to one- fifth of what Elena paid and one-tenth of what Ana paid will make it P 40.00, and the sum of what Maria paid increased by one-eighth of what Elena paid diminished by 1/4 of what Ana paid will give a total of P 70.00. How much did each pay?
Transcribed Image Text:For a cost of P 100.00, a box of apples was jointly purchased by Maria, Elena and Ana. One-half of what Maria paid added to one- fifth of what Elena paid and one-tenth of what Ana paid will make it P 40.00, and the sum of what Maria paid increased by one-eighth of what Elena paid diminished by 1/4 of what Ana paid will give a total of P 70.00. How much did each pay?
Let the amount contributed be M, E and A respectively M + E + A = 100......... ..i) 0.5M + 0.2E + 0.1A = 40.......ii) %3D M+0.125E-0.25A = 70......iii) .... ... .. i - 2*ii would lead to - 0.6E + 0.8A = 20 or A = (20 - 0.6E)/0.8.....iv i- iii -{ 0.875E + 1.25A = 30 %3D replace A with iv 0.875E + 1.25*(20 - 0.6E)/0.8 = 30 0.7E + 25 - 0.75E = 24 E = 20 put this in iv A = (20-0.6*20)/0.8 = 10 %3D
Transcribed Image Text:Let the amount contributed be M, E and A respectively M + E + A = 100......... ..i) 0.5M + 0.2E + 0.1A = 40.......ii) %3D M+0.125E-0.25A = 70......iii) .... ... .. i - 2*ii would lead to - 0.6E + 0.8A = 20 or A = (20 - 0.6E)/0.8.....iv i- iii -{ 0.875E + 1.25A = 30 %3D replace A with iv 0.875E + 1.25*(20 - 0.6E)/0.8 = 30 0.7E + 25 - 0.75E = 24 E = 20 put this in iv A = (20-0.6*20)/0.8 = 10 %3D
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