Kayla’s mom is planning her birthday party. She has a budget of $150. She knows that the food will cost $5 per person. Twelve friends are coming to the party. Which expression represents the amount of money, m , Kayla’s mom has to spend on each guest’s goody bag?(1 point)
Responses
5(m+12)=150
5 Left Parenthesis m plus 12 Right Parenthesis equals 150
12m+5=150
12 m plus 5 equals 150
12(m+5)=150
12 Left Parenthesis m plus 5 Right Parenthesis equals 150
m+12(5)=150
To solve the equation −2(4−n)=24, we can start by simplifying the expression inside the parentheses:
4 - n
Next, we can distribute -2 to each term inside the parentheses:
-2 * 4 - (-2) * n
This simplifies to:
-8 + 2n
Now, we set this expression equal to 24 and solve for n:
-8 + 2n = 24
To isolate the variable, we can add 8 to both sides:
-8 + 8 + 2n = 24 + 8
This simplifies to:
2n = 32
Finally, divide both sides by 2 to solve for n:
2n/2 = 32/2
This gives us:
n = 16
So, the solution to the equation −2(4−n)=24 is n = 16.
To solve this problem, let's set up an equation based on the given information.
Let's say the number we are trying to find is represented by x.
According to the problem statement, "One-quarter of the difference of a number and 3 is 2."
One-quarter of the difference of a number and 3 can be written as (1/4)(x - 3).
We are told that this expression is equal to 2:
(1/4)(x - 3) = 2
To solve the equation, we can start by multiplying both sides by 4 to eliminate the fraction:
4 * (1/4)(x - 3) = 2 * 4
This simplifies to:
x - 3 = 8
Next, we can isolate x by adding 3 to both sides of the equation:
x - 3 + 3 = 8 + 3
This simplifies to:
x = 11
Therefore, the number is 11.
To solve the equation 2/3(x − 6) = 14, we can start by isolating the variable x.
To do this, let's begin by distributing the 2/3 to the terms inside the parentheses:
2/3(x - 6) = 14
2/3 * x - 2/3 * 6 = 14
Simplifying further, we have:
2/3x - 12/3 = 14
Next, let's simplify the equation by converting the fractions to a common denominator:
2/3x - 4 = 14
Now, let's get rid of the -4 on the left side of the equation by adding 4 to both sides:
2/3x - 4 + 4 = 14 + 4
This simplifies to:
2/3x = 18
To solve for x, we can multiply both sides by the reciprocal of 2/3, which is 3/2:
(2/3x)(3/2) = 18(3/2)
This gives us:
x = 54/2
Simplifying further, we have:
x = 27
Therefore, the solution to the equation 2/3(x − 6) = 14 is x = 27.
Given the equation 8(n+6)=104 , identify the real-world problem that corresponds to this equation.
The real-world problem that corresponds to the equation 8(n+6)=104 is a situation where a person has a certain number of items and wants to distribute them equally among a group of people while ensuring that the total number of items is equal to 104.
explain
In this real-world problem, the unknown variable n represents the number of people in the group. The expression (n+6) represents the total number of items that need to be divided equally among the people. The equation 8(n+6)=104 is set up to represent the situation where there are 8 items for each person. The left side of the equation, 8(n+6), represents the total number of items when each person receives 8 items. The right side of the equation, 104, represents the total number of items available. By setting up and solving this equation, we can determine the number of people (or the value of n) in the group that satisfies the condition of having 8 items per person and a total of 104 items.
Solve −2(4−n)=24 (1 point)
Responses
8
8
16
16
−16
negative 16
−8
One-quarter of the difference of a number and 3 is 2. Find the number.(1 point)
Responses
20
20
312
3 and 1 half
54
5 fourths
11
Solve 2/3(x −6)=14 (1 point)
Responses
−15
negative 15
−27
negative 27
27
27
15