Here are two stories:
The initial freshman class at a college is 10% smaller than last year’s class. But then during the first week of classes, 20 more students enroll. There are then 830 students in the freshman class.
A store reduces the price of a computer by $20. Then during a 10% off sale, a customer pays $830.
Here are two equations:
0.9x+20=830
0.9(x−20)=830
Decide which equation represents each story.
Explain why one equation has parentheses and the other doesn’t.
Solve each equation, and explain what the solution means in the situation.
Here are two stories: The initial freshman class at a college is 10% smaller than last year’s class. But then during the first week of classes, 20 more students enroll. There are then 830 students in the freshman class. A store reduces the price of a computer by$20. Then during a 10% off sale, a customer pays$830. Here are two equations: a. Decide which equation represents each story. b. Explain why one equation has parentheses and the other doesn’t. c. Solve each equation, and explain what the solution means in the situation.
but t=what is the anwnser
Equation 0.9x + 20 = 830 represents the first story about the freshman class, while equation 0.9(x−20) = 830 represents the second story about the computer sale.
The equation with parentheses, 0.9(x−20) = 830, uses the parentheses to denote that the 10% off or discount is applied after reducing the price of the computer by $20. The parentheses indicate that the quantity inside should be evaluated first before multiplying by 0.9.
Now let's solve each equation:
For the first equation, 0.9x + 20 = 830:
By subtracting 20 from both sides, we get:
0.9x = 810
Then dividing both sides by 0.9, we have:
x = 900
The solution x = 900 means that the initial freshman class size was 900 students before 20 more students enrolled. This aligns with the information given that the class started out 10% smaller than the previous year's class.
For the second equation, 0.9(x−20) = 830:
We can distribute the 0.9 into the parentheses:
0.9x - 18 = 830
Next, by adding 18 to both sides, we have:
0.9x = 848
Dividing both sides by 0.9:
x = 942.22
The solution x = 942.22 means that the original price of the computer before the $20 reduction was $942.22. This aligns with the information given that during the 10% off sale, the customer paid $830, suggesting that $942.22 was the original price.
The equation 0.9x + 20 = 830 represents the story of the initial freshman class at a college. The equation 0.9(x − 20) = 830 represents the story of the store reducing the price of a computer.
In the equation 0.9x + 20 = 830, there are no parentheses because the operation being done is addition. In this story, we're adding 20 to a percentage of the previous year's freshman class to get the current class size.
In the equation 0.9(x − 20) = 830, there are parentheses because we're multiplying a value by a quantity inside the parentheses. In this story, we're reducing the original price of a computer by $20 and then applying a 10% discount.
To solve the first equation, we can start by subtracting 20 from both sides to isolate 0.9x:
0.9x = 830 - 20
0.9x = 810
Next, divide both sides by 0.9 to solve for x:
x = 810 / 0.9
x = 900
The solution, x = 900, represents the initial size of the freshman class before any students enrolled. This means that last year's class had 900 students.
To solve the second equation, we can start by distributing the 0.9 to the terms inside the parentheses:
0.9x - 0.9(20) = 830
0.9x - 18 = 830
Next, we can add 18 to both sides to isolate 0.9x:
0.9x = 830 + 18
0.9x = 848
Then, divide both sides by 0.9 to solve for x:
x = 848 / 0.9
x ≈ 942.22
The solution, x ≈ 942.22, represents the original price of the computer before the $20 reduction. This means that the original price of the computer was approximately $942.22.
In summary, the equation 0.9x + 20 = 830 represents the story of the initial college freshman class, and the equation 0.9(x − 20) = 830 represents the story of the store reducing the price of a computer. The parentheses are used in the second equation because it involves multiplying a value by a quantity inside the parentheses. The solutions to each equation represent the initial class size and the original price of the computer, respectively.
THe computer scenerio is the second example. It is the second equation because there is a 20$ discount on each computer sold, then a further 10% is taken off (thus making the cost at 90% of the original cost)
0.9(x - 20) = 830
when you solve this you distribute the 0.9 into the brackets (that is times it in)
0.9(x) - 20(0.9) = 830
0.9x - 18 = 830
then add 18 to both sides
0.9x - 18 + 18 = 830 +18
and then you finish and solve for x : )