Half the sum of a number and 10 is 8. Find the number.(1 point)
Responses
3
3
6
6
2
2
-2
-2
To find the number, we can set up the equation "half the sum of a number and 10 is 8" as:
(1/2)(x + 10) = 8
Now, we can solve for x by multiplying both sides of the equation by 2 to eliminate the fraction:
x + 10 = 16
Next, we can isolate x by subtracting 10 from both sides:
x = 6
Therefore, the number is 6.
To find the number, we need to solve the equation given:
"Half the sum of a number and 10 is 8."
Let's break down the equation:
The sum of a number and 10 is written as "(number + 10)."
Half of this sum is written as "(1/2) * (number + 10)."
According to the equation, this half sum is equal to 8; thus, we can write the equation:
(1/2) * (number + 10) = 8
To solve for the number, we can follow these steps:
1. Multiply both sides of the equation by 2 to remove the fraction:
2 * (1/2) * (number + 10) = 2 * 8
Simplifying gives us:
number + 10 = 16
2. Subtract 10 from both sides of the equation to isolate the number:
number + 10 - 10 = 16 - 10
Simplifying further gives us:
number = 6
Therefore, the number is 6.
John buys 8 packs of cookies at the grocery store. The cookies are on sale for 50 cents off per pack. He spends $20. Which equation can be used to find the original cost of a box of cookies, c?(1 point)
Responses
8(c+0.50)=208 times open paren c plus 0 point 5 0 close paren is equal to 20
8c−0.50=208 c minus 0 point 5 0 is equal to 20
8(c−0.50)=208 times open paren c minus 0 point 5 0 close paren is equal to 20
8−0.50c=20
The correct equation to find the original cost of a box of cookies, c, is:
8(c - 0.50) = 20.
Given the equation 8(n+6)=104, identify the real-world problem that corresponds to this equation.(1 point)
Responses
The real-world problem that corresponds to the equation 8(n+6)=104 is not provided.
Which equation corresponds to the following problem?
(1 point)
Responses
8(2n+6)=1048 times open paren 2 n plus 6 close paren is equal to 104
8(n+6)=1048 times open paren n plus 6 close paren is equal to 104
2n+6=82 n plus 6 is equal to 8
8+n+n+6=104
The equation that corresponds to the given problem is: 8(n+6)=104
Consider this equation:
4(3x−2)=−24
Part 1. What is your first step in solving this equation? Remember, there is more than one way to solve this equation.
Part 2. How would you isolate the variable and solve for x after you have completed Part 1?
You do not need to solve the problem. Simply, describe your process.
**Please label Part 1 and Part 2 in your answer.**
Part 1: The first step in solving this equation is to distribute the 4 to each term inside the parentheses. This can be done using the distributive property.
Part 2: After distributing the 4, the equation becomes 12x - 8 = -24. To isolate the variable, we can add 8 to both sides of the equation to move the -8 term to the right side. This gives us 12x = -16. Finally, to solve for x, we divide both sides of the equation by 12, resulting in x = -16/12 or x = -4/3.
Stan took Lily to his friend’s restaurant on a date. The friend told the waiter to remove the $12 dessert from Stan’s bill. Stan tipped the waiter 20% on the reduced bill, which was a $15 tip. Fill in the blanks to write an equation that will determine the amount of the original bill, b
Let's assume the original bill was b dollars.
According to the problem, the dessert worth $12 was removed from Stan's bill. Therefore, his reduced bill would be (b - 12) dollars.
Stan tipped the waiter 20% on the reduced bill, which was a $15 tip.
We can write this information as:
0.2(b - 12) = 15
This equation represents the amount of the original bill, b, given the information provided.
Molly has 6 grandchildren. She likes to be fair and buy gifts for all of them at the same time. She found jigsaw puzzles, each discounted by 50¢. Find the original cost of each puzzle if she spent a total of $27.(1 point)
Each puzzle cost $
Let's assume that the original cost of each puzzle is x dollars.
Molly found jigsaw puzzles, and each was discounted by 50¢, which means each puzzle cost (x - 0.50) dollars.
She has 6 grandchildren, so she bought a total of 6 puzzles.
The total cost of all the puzzles can be calculated by multiplying the cost of each puzzle by the number of puzzles:
6 * (x - 0.50) = $27
Simplifying the equation:
6x - 3 = $27
To solve for x, we'll isolate x by adding 3 to both sides of the equation:
6x - 3 + 3 = $27 + 3
Simplifying further:
6x = $30
Finally, to find the cost of each puzzle, we'll divide both sides of the equation by 6:
x = $30 / 6
x = $5
Therefore, each puzzle originally cost $5.
Ethan had 7 of his friends over. He ordered cheese pizzas and mozzarella sticks for the 8 of them. In all, there were 64 pieces of food. If each person had 5 slices of pizza, find the number of mozzarella sticks each person ate.(1 point)
Each person ate
mozzarella sticks.
Let's assume that each person ate x mozzarella sticks.
There were 8 people in total, so the number of mozzarella sticks eaten can be calculated by multiplying the number of people by the number of mozzarella sticks each person ate:
8 * x = 64
To solve for x, we'll isolate x by dividing both sides of the equation by 8:
x = 64 / 8
x = 8
Therefore, each person ate 8 mozzarella sticks.
Jason’s age is 12 the difference of his mother’s age and 6. Jason is 16. How old is Jason’s mother
Let's assume Jason's mother's age is represented by the variable "M".
According to the information given, Jason's age is 12 and the difference between his mother's age and 6. We can write this as an equation:
M - 6 = 12
To find Jason's mother's age, we need to solve for M. We can do this by isolating M by adding 6 to both sides of the equation:
M - 6 + 6 = 12 + 6
Simplifying, we get:
M = 18
Therefore, Jason's mother is 18 years old.
To find the number, we'll set up an equation based on the given information.
Let's call the number "x".
According to the problem, half the sum of the number and 10 is 8. We can write this as:
0.5(x + 10) = 8
To solve this equation, we'll first distribute the 0.5:
0.5x + 5 = 8
Next, we'll subtract 5 from both sides of the equation to isolate the 0.5x:
0.5x = 8 - 5
Simplifying:
0.5x = 3
Finally, to solve for x, we'll divide both sides of the equation by 0.5:
x = 3 ÷ 0.5
Evaluating this expression:
x = 6.
Therefore, the number is 6.