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 :) and im sorry i reposted this
a. 4(x+3.2) = 124.8
Solve for x.
b. I cannot model.
c. 5(x-2.75) = 29.50
Solve for x.
No problem, I'm here to help! Let's tackle these word problems with a touch of humor:
1. Okay, let's square off against this problem! The perimeter of the larger square is 124.8 cm, and its sides are 3.2 cm longer than those of the small square. So we can set up the equation: Perimeter = 4 * Side Length, right? But since the sides of the larger square are longer, we need to add 3.2 to the side length of the small square. Thus, we have the equation 124.8 = 4 * (s + 3.2). Now, it's time for algebra to save the day and solve for s!
2. Fore! Valerie got a sweet deal on golf balls! She bought five packages for $29.50, and each package had a discount of $2.75. To find out the regular price, we can set up an equation. Let's call the regular price R. With a discount of $2.75, the sale price of each package is R - $2.75. Since Valerie bought five packages, the total sale price is 5 * (R - $2.75), which is equal to $29.50. Now we just have to solve this equation and give a high-five to math!
So, are you ready to solve these problems like a boss?
No problem! I can help you with these word problems step by step. Let's start with the first one:
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) To represent the situation with an equation of the form a(x + b) = c, we need to consider the perimeter of the larger square. The perimeter of a square is given by multiplying the side length by 4. So, for the larger square, we can write the equation:
4(s + 3.2) = 124.8
Let's solve this equation to find the side length of the smaller square.
4s + 12.8 = 124.8
4s = 124.8 - 12.8
4s = 112
s = 112/4
s = 28
Therefore, the side length of the smaller square is 28 cm.
b) Now, let's verify this solution by using a model. We can draw two squares, one representing the small square and the other representing the larger square. Since the sides of the larger square are 3.2 cm longer, we can add four small segments of 3.2 cm to each side of the smaller square. Then we can calculate the perimeter of the larger square and see if it matches the given value of 124.8 cm.
Side length of the smaller square = 28 cm
Side length of the larger square = 28 + 3.2 = 31.2 cm
Perimeter of the larger square = (31.2 cm × 4) = 124.8 cm
Therefore, the solution is verified.
Now, let's move on to the second problem:
2. Valerie bought five packages of golf balls on sale for $29.50. Each package had a discount of $2.75. We need to write and solve an equation to determine the regular price of each package.
Let's let x be the regular price of each package. Since each package has a discount of $2.75, the equation can be set up as:
5(x - $2.75) = $29.50
Step 1: Distribute the 5 to each term inside the parentheses.
5x - (5 × $2.75) = $29.50
5x - $13.75 = $29.50
Step 2: Add $13.75 to both sides of the equation.
5x - $13.75 + $13.75 = $29.50 + $13.75
5x = $43.25
Step 3: Divide both sides of the equation by 5.
(5x)/5 = $43.25/5
x = $8.65
Therefore, the regular price of each golf ball package is $8.65.
I hope this helps! Let me know if you have any more questions.
No problem! I'll be happy to help you with these word problems.
1. To solve this problem, let's break it down step by step:
a) We're given that the larger square has a perimeter of 124.8 cm. Let's denote the side length of the smaller square as s. The sides of the larger square are 3.2 cm longer than those of the small square, so the side length of the larger square would be s + 3.2 cm.
The perimeter of a square is calculated by adding up the lengths of all its sides. In this case, the perimeter of the larger square is 124.8 cm. We can represent this situation with the equation:
Perimeter of larger square = 4 × side length of larger square = 124.8 cm.
Using the information we have, we can substitute the values into the equation:
4(s + 3.2) = 124.8.
Now, we can solve the equation to find the value of s.
b) To verify our solution, we can use a model. We can draw two squares, one representing the larger square and the other representing the smaller square. Then, we can compare the side lengths and check if the larger square's perimeter is indeed 124.8 cm.
2. Let's solve the second problem together:
Valerie bought five packages of golf balls on sale for $29.50. Each package had a discount of $2.75. We need to determine the regular price of each package.
Let's denote the regular price of each package as x (in dollars). Since there are five packages, the total amount Valerie paid after the discount was applied is $29.50.
We can express this situation with an equation:
Regular price × Number of packages − Discount per package × Number of packages = Total amount paid.
Substituting the given values:
x × 5 − $2.75 × 5 = $29.50.
Now, we can solve this equation to find the regular price (x).