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inn [45]
3 years ago
13

Sebastian is working to summer jobs, making $8 per hour walking dogs and $10 per hour clearing tables. In a given week, he can w

ork no more than 12 total hours and must earn a minimum of $100. If X represents the number of hours walking dogs and Y represents the number of hours clearing tables, right and solve a system of inequalities graphically and determine one possible solution.

Mathematics
1 answer:
True [87]3 years ago
8 0

Answer:

The graph in the attached figure

One possible solution is the ordered pair (3,8)

see the explanation

Step-by-step explanation:

Let

x ---> the number of hours walking dogs

y ----> the number of hours clearing tables

we know that

He can work no more than 12 total hours

so

x+y\leq 12 ----> inequality A

He must earn a minimum of $100

so

8x+10y\geq 100 ----> inequality B  

Solve the system of inequalities by graphing

using a graphing tool

The solution is the triangular shaded area

see the attached figure

Remember that

If a ordered pair is a solution of the system of inequalities, then the ordered pair must lie in the shaded area of the solution set (the ordered pair makes true both inequalities)

so

One possible solution is the ordered pair (3,8)

That means

In the given week, the number of hours walking dogs was 3 and the number of hours clearing tables was 8

<u><em>Verify algebraically</em></u>

Substitute the value of x and the value of y in the inequality A and in the Inequality B

<em>inequality A</em>

3+8\leq 12

11\leq 12 ----> is true

<em>Inequality B</em>

8(3)+10(8)\geq 100

104\geq 100 ---> is true

therefore

the ordered pair (3,8) is a possible solution of the system

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Step-by-step explanation:

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Convert the following decimals 1 / 8
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Previous
Natali5045456 [20]

Answer: y = 5d + 7 / c - 3

Step-by-step explanation:

Step 1: Add -3y to both sides

cy - 7 + -3y = 5d + 3y + -3y

= cy - 3y - 7 = 5d

Step 2: Now, add 7 on both sides

cy - 3y - 7 +7 = 5d +7

= cy - 3y = 5d +7

Step 3: Factor out y

y(c - 3) = 5d + 7

Step 4: Divide both sides by c-3

y(c - 3) / c - 3 = 5d+7 / c-3

Your answer for this should be

y = 5d + 7 / c - 3

Hope this helped!

3 0
3 years ago
A club raises $3,207 to buy stuffed animals for a local children's hospital. Each stuffed animal costs $17. What is the maximum
Ksju [112]

Answering:

188

Explaining:

To solve this problem, we must divide the total amount of money raised by the cost of the stuffed animals. Each stuffed animal costs $17. The club raised $3,207 to buy said stuffed animals. By dividing the money earned, which is also the money the club is able to spend, by the cost of a single/one stuffed animal, we will get how many stuffed animals the club can purchase with the money they currently possess. Our equation will look like this: 3,207 ÷ 17.

After dividing 3,207 by 17, we have the number 188.64705882. This can be rounded to the nearest tenth to create the simpler yet still accurate number 188.6.

Our final step is to round 188.6 down to the whole number it already has. (That is to say, simply cut off the fraction and remove it to get our answer.) This step must be done because we are buying stuffed animals in a real-world situation. The club would not be able to purchase part of a stuffed animal for a fraction of the cost, and the cost of the stuffed animals in the problem is a fixed value. This means that the fraction is irrelevant since we cannot purchase anything with it, effectively making it totally irrelevant to the answer. After removing the fraction from 188.6, we are left with 188.

Therefore, the maximum number of stuffed animals the club can buy is <em>188 stuffed animals</em>.

4 0
2 years ago
3(4x-7)=27<br> What does x =?<br> Please help asap im timed!!!
Scilla [17]

Answer:

x = 4

Step-by-step explanation:

3 x ( 4x -7 ) = 27

3 x 4x = 12x

3 x -7 = -21

12x -21 = 27

12x -21 + 21 = 27 + 21

12x = 48

12x/12 = 48/12

x = 4

3 0
3 years ago
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