Question

Hi! 15+ points for this! :D

1. Alex has $40, and Ellen has $24. Alex is saving $6 per day, and Ellen is saving $10 day. After how many days will Alex and Ellen have the same amount of money?

2. Kendra owns a restaurant. She charges $6.00 for two eggs and one piece of toast and $3.60 for one egg and one piece of toast. How much does Kendra charge per egg? How much per piece of toast?

3. A restaurant has one type of lemonade that is 30% sugar and another that is 10% sugar. How many gallons of each type does the restraint need to make 4 gallons of a lemonade mixture that is 15% sugar?

4. A scientist has a container of 2% acid solution and a container of 5% acid solution. How many fluid ounces of each concentration should be combined to make 25 fl oz of 3.2% acid solution?





16. The speed of a kayaker is 5.75 mi/h paddling with the river current and 3.25 mi/h paddling against it. What is the speed of the river current?

Susan make $12 per hour babysitting and $24 per hour as a lifeguard. Her goal is to make at least $420. Write an inequality, graph the solution, and list three possible solutions

25. Joe wants to fence a rectangular pen for his goats. The length of the pen should be at least 40 ft, and the distance around should be no more than 150 ft. Write a systems of inequalities and graph to represent the possible dimensions of the pen.

Answer 1

1. 4 days

2. $1.2

3. 1 and 3 gallons

4. 15 and 10

16. 1.2 mi/h

-- Please refer to graph

-- Please refer to graph

Explanation:

Solution 1.

Alex has $40, and Ellen has $24. Alex is saving $6 per day, and Ellen is saving $10 day.

Let x be the number of days in which they both have same money:

As per given statement:

`40 + 6x=24+10x\\\Rightarrow 4x = 16\\\Rightarrow x =4`

In 4 days, they will have same money.

Solution 2:

Kendra owns a restaurant. She charges $6.00 for two eggs and one piece of toast and $3.60 for one egg and one piece of toast.

Let x be the price of one egg.

Let y be the price of one toast.

As per given statement:

`2x+y=6 ...... (1)\\x+y= 3.6 ...... (2)`

Subtracting (2) from (1):

`\Rightarrow x = \$2.4`

Price of toast = 3.6 - 2.4 = $1.2

Solution 3:

A restaurant has one type of lemonade that is 30% sugar and another that is 10% sugar. Resultant mixture 4 gallons of 15% sugar.

Let x be the amount of lemonade with 30% sugar.

Amount of another lemonade with 10% sugar = (4-x)

As per question statement:

`x * 30\% + (4-x) * 10\% = 4 * 15\%\\\Rightarrow x * 30 + (4-x) * 10 = 4 * 15\\\Rightarrow 20x = 20\\\Rightarrow x = 1`

Lemonade with 30% sugar required is 1 gallon.

Lemonade with 10% sugar required is 3 gallons.

Solution 4:

A scientist has a container of 2% acid solution and a container of 5% acid solution. Resultant mixture is 25 fl oz of 3.2%.

Let x be the amount of 2% acid solution.

Amount of another lemonade with 5% acid solution = (25-x)

As per given question statement:

`2\%\ of\ x + 5\% \ of\ (25-x) = 3.2\%\ of\ 25\\\Rightarrow 2x + 5(25-x)=3.2 * 25\\\Rightarrow -3x = -1.8 * 25\\\Rightarrow x = 15`

2% acid solution required is 15 fl oz.

5% acid solution required is 10 fl oz.

Solution 16:

Let v be the speed of river current.

Let u be the speed of kayaker.

As per question:

The speed of a kayaker is 5.75 mi/h paddling with the river current and 3.25 mi/h paddling against it.

`u +v=5.75......(1)\\u-v = 3.25.....(2)`

Equation (1) - (2):

`2v = 2.5\\\Rightarrow v = 1.25\ mi/h`

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Susan make $12 per hour babysitting and $24 per hour as a lifeguard. Her goal is to make at least $420.

Let x be the number of hours for babysitting.

Let y be the number of hours as lifeguard.

As per given statement:

`12x+24y > 240`

Please refer to graph attached with file name: Inequality

Three possible solutions: (20,20), (21,21) and (22,22)

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25. Joe wants to fence a rectangular pen for his goats. The length of the pen should be at least 40 ft, and the distance around should be no more than 150 ft

Let x be length

and y be width.

As per statement:

x > 40

And perimeter should be less than equal to 240.

2(x+y)
`\leq` 240

Please refer to attached graph with name: "2EquationInq"

Possible dimensions of pen can be (50,20).