BIG IDEAS MATH Algebra 1: Common Core Student Edition 2015

1st Edition

ISBN: 9781608408382

Author: HOUGHTON MIFFLIN HARCOURT

Publisher: Houghton Mifflin Harcourt

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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 3.4, Problem 24E

(a)

To determine

To graph: The equation 10x+12y=300 and also interpret the intercepts.

(a)

Expert Solution

Explanation of Solution

Given

The equation is 10x+12y=300 .

Find the coordinates of the equation 10x+12y=300 to graph the equation.

Substitute 0 for x in the equation 10x+12y=300 to obtain the value of y .

10(0)+12y=30012y=300y=30012=25

Now, substitute 10 for x in the equation 10x+12y=300 to obtain the value of y .

10(10)+12y=30012y=300−100y=20012=16.16

Substitute 0 for y in the equation 10x+12y=300 to obtain the value of x .

10x+12(0)=30010x=300x=30010=30

Therefore, the coordinates of the equation are (0,25),(30,0),(10,16.16) .

Draw the graph of the equation 10x+12y=300 as shown in Figure 1.

BIG IDEAS MATH Algebra 1: Common Core Student Edition 2015, Chapter 3.4, Problem 24E

The x -intercepts are the points where the value of y=0 and the y -intercepts are the points where the value of x=0 .

Therefore, it can be observed from Figure 1 that the x -interpret is (30,0) and the y - intercept is (0,25) .

Interpretation:

The graph does not pass through the origin.

(b)

To determine

To find: The number of long-sleeved shirts to order if twelve students order short sleeved shirts.

(b)

Expert Solution

Answer to Problem 24E

The person can order 15 long sleeved shirts .

Explanation of Solution

Given:

The equation is 10x+12y=300 and twelve students demand for short sleeved shirts.

Calculation:

It is given that twelve students demand for short sleeved shirts.

And it is also given that x is the number of short sleeved shirts and y is the number of long sleeved shirts.

There is need to find the value of y for when x=12 .

Substitute 0 for y in the equation 10x+12y=300 to obtain the value of x .

10(12)+12y=30012y=300−120y=18012=15

Therefore, there are 15 long sleeved shirts need to order.

Conclusion:

Thus, the person can order 15 long sleeved shirts .

Chapter 3.4, Problem 23E

Chapter 3.4, Problem 25E

Chapter 3 Solutions

BIG IDEAS MATH Algebra 1: Common Core Student Edition 2015

Ch. 3.1 - Prob. 1E Ch. 3.1 - Prob. 2E Ch. 3.1 - Prob. 3E Ch. 3.1 - Prob. 4E Ch. 3.1 - Prob. 5E Ch. 3.1 - Prob. 6E Ch. 3.1 - Prob. 7E Ch. 3.1 - Prob. 8E Ch. 3.1 - Prob. 9E Ch. 3.1 - Prob. 10E

Ch. 3.1 - Prob. 11E Ch. 3.1 - Prob. 12E Ch. 3.1 - Prob. 13E Ch. 3.1 - Prob. 14E Ch. 3.1 - Prob. 15E Ch. 3.1 - Prob. 16E Ch. 3.1 - Prob. 17E Ch. 3.1 - Prob. 18E Ch. 3.1 - Prob. 19E Ch. 3.1 - Prob. 20E Ch. 3.1 - Prob. 21E Ch. 3.1 - Prob. 22E Ch. 3.1 - Prob. 23E Ch. 3.1 - Prob. 24E Ch. 3.1 - Prob. 25E Ch. 3.1 - Prob. 26E Ch. 3.1 - Prob. 27E Ch. 3.1 - Prob. 28E Ch. 3.1 - Prob. 29E Ch. 3.1 - Prob. 30E Ch. 3.1 - Prob. 31E Ch. 3.1 - Prob. 32E Ch. 3.1 - Prob. 33E Ch. 3.1 - Prob. 34E Ch. 3.1 - Prob. 35E Ch. 3.1 - Prob. 36E Ch. 3.1 - Prob. 37E Ch. 3.1 - Prob. 38E Ch. 3.1 - Prob. 39E Ch. 3.1 - Prob. 40E Ch. 3.1 - Prob. 41E Ch. 3.1 - Prob. 42E Ch. 3.1 - Prob. 43E Ch. 3.1 - Prob. 44E Ch. 3.1 - Prob. 45E Ch. 3.1 - Prob. 46E Ch. 3.1 - Prob. 47E Ch. 3.1 - Prob. 48E Ch. 3.1 - Prob. 49E Ch. 3.1 - Prob. 50E Ch. 3.1 - Prob. 51E Ch. 3.2 - Prob. 1E Ch. 3.2 - Prob. 2E Ch. 3.2 - Prob. 3E Ch. 3.2 - Prob. 4E Ch. 3.2 - Prob. 5E Ch. 3.2 - Prob. 6E Ch. 3.2 - Prob. 7E Ch. 3.2 - Prob. 8E Ch. 3.2 - Prob. 9E Ch. 3.2 - 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To graph: The equation 10 x + 12 y = 300 and also interpret the intercepts.

Concept explainers

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To graph: The equation 10x+12y=300 and also interpret the intercepts.

Explanation of Solution

To find: The number of long-sleeved shirts to order if twelve students order short sleeved shirts.

Answer to Problem 24E

Explanation of Solution

Chapter 3 Solutions