Explanation Given: In box A , there are 12 oranges, 5 grapefruits and 3 tangerines. In box B , there are 10 oranges, 6 grapefruits and 4 tangerines. In box B , there are 5 oranges, 8 grapefruits and 5 tangerines. There are 91 oranges, 63 grapefruits and 40 tangerines available. Calculation: Consider the number of box A be x , the number of box B be y and the number of box C be z . Write the equation for total oranges, when there are 12, 10 and 5 oranges in box A, B and C . Substitute the value of z in terms of x and y . 12 x + 10 y + 5 z = 91 z = 91 − ( 12 x + 10 y ) 5 …… (1) Write the equation for total grapefruit, when there are 5, 6 and 8 grapefruit in box A, B and C . Substitute 91 − ( 12 x + 10 y ) 5 for z, in the equation. 5 x + 6 y + 8 z = 63 From the equation (1) the above equation is written as, 5 x + 6 y = 63 − 8 z 5 x + 6 y = 63 − 8 ( 91 − ( 12 x + 10 y ) ) 5 25 x + 30 y = 315 − 728 + 96 x + 80 y − 71 x − 50 y = − 413 …… (2) Write the equation for total tangerines, when there are 3, 4 and 5 tangerines in box A, B and C . Substitute 91 − ( 12 x + 10 y ) 5 for z, in the equation. 3 x + 4 y + 5 z = 40 From the equation (1) the above equation is written as, 3 x + 4 y = 40 − 5 z 3 x + 4 y = 40 − 5 ( 91 − ( 12 x + 10 y ) 5 ) 3 x + 4 y = 40 − 91 + 12 x + 10 y − 9 x − 6 y = − 51 Divide the equation by − 3 , ( − ( 9 x + 6 y ) ) − 3 = − 51 − 3 3 x + 2 y = 17 …… (3) Multiply the equation (3) by 25, ( 3 x + 2 y ) 25 = 17 ( 25

8th Edition

ISBN: 9780134178967

Author: John Tobey Jr., Jeffrey Slater, Jamie Blair, Jenny Crawford

Publisher: PEARSON

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Chapter 4.3, Problem 31E

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To calculate: The number of gift boxes A, B, and C for the 91 oranges, 63 grape fruits, and 40 tangerines required.

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Chapter 4.3, Problem 30E

Chapter 4.3, Problem 32E

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The number of gift boxes A , B , and C for the 91 oranges, 63 grape fruits, and 40 tangerines required.

Solution Summary: The author calculates the number of gift boxes A, B, and C for 91 oranges, 63 grapefruits and 40 tangerines.

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To calculate: The number of gift boxes A, B, and C for the 91 oranges, 63 grape fruits, and 40 tangerines required.

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Chapter 4 Solutions