Explanation 1) Concept: The theoretical statement can be converted into a mathematical statement by assuming some variable for the unknowns in the statement and by applying suitable algebraic method, the value of the unknown in the statement can be obtained. Solving an expression is to find the value of unknown in the expression, which on substitution must satisfy the expression. 2) Calculation: Given, Amount expected = $ 490 Current price for the can per hundred pounds } = $ 4 Quantity of cans that the group already had } = 12, 000 lb Rate of collecting the cans by the group per day } = 400 lb per day Rate at which the price was lowered } = $ 0 .10 per hundred pounds per day Let ‘ x ’ be the number of days that the group should wait to get the expected amount of $ 490. Quantity of cans that they already have } = 12, 000 lb Quantity of cans that the group will collect in ' x ' numbers of days at the rate of 400 lb per day } = 400 x lb Hence, the total quality of cans that the qroup will hare in ' x ' number of days } = ( 12 , 000 + 400 x ) lb Current price of the can = $ 4 per hundred pounds Price lowered per day = $ 0 .10 per hundred pounds Price lowered by x number of days } = $ 0.10 x per hundred pounds Hence, the price that the group will get for the can after ' x ' number of days } = $ ( 4 − 0.10 x ) per hundred pounds Thus, the amount that the group will get after ' x ' number of days } = Total quantity of can, that the group will have on the day ' x ' } × { Price for the can, that the group will get on the day ' x ' The total amount = ( 12 , 000 + 400 x ) ( 4 − 0.10 x 100 ) But as the expected amount is $ 490 We have, 490 = ( 12 , 000 + 400 x ) ( 4 − 0.10 x ) 100 Multiply 100 on both sides, 490 ( 100 ) = ( 100 ) ( 12 , 000 + 400 x ) ( 4 − 0.10 x ) 100 49 , 000 = ( 12000 + 400 x ) ( 4 − 0

Essentials of College Algebra (11th Edition)

11th Edition

ISBN: 9780321912251

Author: Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels

Publisher: PEARSON

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Question

Chapter 1.5, Problem 58E

To determine

To find:

The number of days that the local group of scouts should wait in order to receive $490 for their cans, the group has already collected 12, 000 lb of cans, for which they could currently receive $4 per hundred pounds. The group can continue to collect cans at the rate of 400lb per day. However, a glut in the old can market has caused the recycling company to announce that it will lower its price, starting immediately, by $0.10 per hundred pounds per day, the scouts can make only one trip to the recycling center.

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Chapter 1.5, Problem 57E

Chapter 1.6, Problem 1E

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Chapter 1 Solutions

Essentials of College Algebra (11th Edition)

Ch. 1.1 - Prob. 1E Ch. 1.1 - Prob. 2E Ch. 1.1 - Prob. 3E Ch. 1.1 - Prob. 4E Ch. 1.1 - Prob. 5E Ch. 1.1 - Prob. 6E Ch. 1.1 - Prob. 7E Ch. 1.1 - Prob. 8E Ch. 1.1 - Prob. 9E Ch. 1.1 - Prob. 10E

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