Hii! I'm kind of stuck on these, they may be simple I have a lot going on because tomorrow is my last day of school, and I need to turn this in tomorrow;;; Can someone help? Please? :,)
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?
5. 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?
6. 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
7. 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.
I'll get you started. If this doesn't help, you are in big trouble.
#1. 40+6x = 24+10x
#2. 2e+t = 6.00
e+t = 3.60
#3. .30x + .10(4-x) = .15(4)
#4. Just like #3
#5. k+c = 5.75
k-c = 3.25
#6. 12b + 24g >= 420
#7. L >= 40
2(L+W) <= 150
I'll help you w/ 5; use above as ref to learn
5.
y = still water
x = current speed
+ for with the water
- for going against the water
elimination
y+x=5.75. (x+ and x- cancel out)
y-x=3.25
--------------
2y=9
/2 /2
y=4.5 (still water)
y+x=5.75
4.5 +x = 5.75
-4.5 -4.5
-----------------
x = 1.25
The current speed is 1.25
Hello! I'd be happy to help you with these questions. I'll explain the steps to solve each one, so you'll be able to do it on your own as well.
1. To find out after how many days Alex and Ellen will have the same amount of money, you need to set up an equation. You can start by setting up the equation: 40 + 6d = 24 + 10d. Here, d represents the number of days. By simplifying and solving for d, you can find the answer.
2. To find out how much Kendra charges per egg and per piece of toast, you need to set up a system of equations. Let's assume x represents the cost per egg and y represents the cost per piece of toast. You can set up the following equations: 2x + y = 6.00 and x + y = 3.60. By solving this system of equations, you can find the values of x and y.
3. To determine how many gallons of each type of lemonade the restaurant needs to make a 15% sugar mixture, you can set up a system of equations. Let's assume x represents the gallons of the 30% sugar lemonade and y represents the gallons of the 10% sugar lemonade. The equations can be set up as follows: x + y = 4 (total gallons) and 0.30x + 0.10y = 0.15(4) (sugar content equation). Solve this system of equations to get the values of x and y.
4. To determine the amounts of the 2% and 5% acid solutions to mix, you can set up a system of equations. Let's assume x represents the amount of 2% acid solution and y represents the amount of 5% acid solution. The equations can be set up as follows: x + y = 25 (total fluid ounces) and 0.02x + 0.05y = 0.032(25) (acid content equation). Solve this system of equations to get the values of x and y.
5. To find the speed of the river current, you can set up a system of equations. Let's assume x represents the speed of the kayaker and y represents the speed of the river current. The equations can be set up as follows: x + y = 5.75 and x - y = 3.25. Solve this system of equations to get the values of x and y.
6. To write an inequality, graph the solution, and list three possible solutions, you can set up an inequality based on Susan's goal. Let's assume x represents the number of hours Susan babysits and y represents the number of hours she lifeguards. You can set up the inequality 12x + 24y >= 420. Graph this inequality on a coordinate plane and then find three possible solutions by picking different points on or above the line.
7. To represent the possible dimensions of the pen with inequalities and graph it, you can set up two inequalities. Let's assume x represents the length of the pen and y represents the width of the pen. You can set up the inequalities x >= 40 and 2(x + y) <= 150. Graph these inequalities on a coordinate plane to visualize the possible dimensions of the pen.
I hope this helps! Let me know if you have any further questions or need any clarification. Good luck with your last day of school and turning in your work!