can someone please help me, i posted this like 3 times. i need help on a couple of questions. I did all my other questions but i need a lot of help with the word problems...
1. The side length of a small square is s. A larger square has a perimeter of 124.8 cm. Its sides are 3.2 cm longer than those of the small square.
a) represent the situation with an equation of the form a(x + b) = c. Then determine the side length of the smaller square.
b.) verify your solution by using a model.
2. Valerie bought five packages of golf balls on sale for $29.50. Each package had a discount of $2.75. Write and solve an equation to determine the regular price of each package.
thanks :)
#1
I read it and thought it was a lot to do about nothing.
side of larger square = 124.8/4= 31.2
31.2 is 3.2 longer than the side of the smaller square
so the side of the smaller square is 28
done!
Make a model ??
#2
each golfball package costs 29.5/5 = $5.90
This $5.90 was after a discount of $2.75
So the regular price of one package was 5.90+2.75 = $8.65
Editorial:
Asking to write the above as an equation, when there is no need for it, makes students dislike math.
THANK YOU SO MUCH!!!!!!!!!!!!!!!!!!!!!
Of course! I'd be happy to help you with your questions.
1. Let's break down the problem step by step:
a) To represent the situation with an equation of the form a(x + b) = c, we need to first determine the variables. Let's think about what we know:
- The side length of the small square is denoted as s.
- The larger square has a perimeter of 124.8 cm, which means each side of the larger square is equal to (124.8 / 4) = 31.2 cm.
- The sides of the larger square are 3.2 cm longer than those of the small square.
Now, let's set up the equation:
a(s + b) = c
In this case:
a = side length of the larger square = 31.2 cm
b = difference in side length between the larger and smaller squares = 3.2 cm
c = perimeter of the larger square = 124.8 cm
So, the equation becomes:
31.2(s + 3.2) = 124.8
Now, let's solve this equation to find the side length of the smaller square.
b) To verify the solution by using a model, we can substitute the obtained value of s back into the equation and check if it satisfies the equation with the given values.
Now let's move on to the next question:
2. To determine the regular price of each package, we'll use an equation. Let's set up the variables:
- The regular price of each package is denoted as p.
- Valerie bought five packages of golf balls for $29.50, which means she paid a total price of $29.50 for all packages.
- Each package had a discount of $2.75.
Now, let's set up the equation:
5p - 5(2.75) = 29.50
Here, we have subtracted the discount for each package (2.75) from the regular price (5p) and equated it to the total amount Valerie paid.
Now, we can solve this equation to find the regular price of each package.
I hope this helps! Let me know if you have any further questions.
I'd be happy to help you with your questions! Let's break them down one by one.
1. For the first question, we need to represent the situation with an equation and determine the side length of the smaller square.
a) Let's start by assigning variables to the side lengths of the small and large squares. We'll use "s" for the small square and "s + 3.2" for the large square (since the sides of the large square are 3.2 cm longer than those of the small square).
The perimeter of a square is calculated by adding up the lengths of all four sides. Since the perimeter of the large square is given as 124.8 cm, we can set up the equation:
Perimeter of large square = 4 * (s + 3.2) = 124.8
To simplify this equation, we can multiply (s + 3.2) by 4:
4s + 12.8 = 124.8
Now, we can solve for s:
4s = 124.8 - 12.8
4s = 112
s = 112 / 4
s = 28
Therefore, the side length of the smaller square is 28 cm.
b) To verify our solution, we can use a model. We can draw two squares, one with a side length of 28 cm (the small square) and another with a side length of 31.2 cm (the large square). Using a ruler, we can measure the squares' perimeters and confirm that they match the given values. This visual representation helps verify our solution.
2. For the second question, we'll write and solve an equation to determine the regular price of each package of golf balls.
Let's say the regular price of each package is "p". Since Valerie bought five packages and each package had a discount of $2.75, the total discount she received is 5 * $2.75 = $13.75.
The total cost after the discount is $29.50, so the equation can be set up as:
5p - $13.75 = $29.50
To solve for the regular price, p, we'll isolate the variable:
5p = $29.50 + $13.75
5p = $43.25
p = $43.25 / 5
p ≈ $8.65
Therefore, the regular price of each package is approximately $8.65.
I hope this helps! If you have any further questions, feel free to ask.