Algebra: Structure And Method, Book 1

(REV)00 Edition

ISBN: 9780395977224

Author: Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole

Publisher: McDougal Littell

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Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

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A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.

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Question

Chapter 1.7, Problem 1P

To determine

To calculate: Solve using the five-step plan. Write out each step. A choice of possible numbers for one unknown is given.An oil painting is 16 years older than a watercolor by the same artists. The oil painting is also three times older than the watercolor. How old each? Choices for the watercolor's age: 4, 8, 12.

Expert Solution & Answer

Answer to Problem 1P

the age of watercolor is a=8 and the age of painting is a+16=8+16=24

Explanation of Solution

Given information:An oil painting is 16 years older than a watercolor by the same artists and the oil painting is also three times older than the watercolor.

Calculation:

Step 1: Here we have two unknowns, age of watercolor and age of painting.

Step 2: Let a be the age of watercolor and (a+16) be the age of the painting.

Step 3: As given, oil painting is three times older than the watercolor such that 16+a=3a

Step 4: Choices for a are given as 4, 8, 12.

a	16+a=3a	True / False
4	16+4=3*4 20≠12	False
8	16+8=3*8 24=24	True
12	16+12=3*12 28≠36	False

From above table we can say that the age of watercolor is a=8 and the age of painting is

a+16=8+16=24

Step 5: Now we verify the answer

An oil painting is 16 years older than a watercolor: 8+16=24 , which is correct

oil painting is three times older than the watercolor: 16+8=3*8=24 , which is also correct.

Chapter 1.6, Problem 3E

Chapter 1.7, Problem 2P

Chapter 1 Solutions

Algebra: Structure And Method, Book 1

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

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