To solve the equation \(-\frac{1}{2}(x + 10) = -3\), the first operation you should do is to eliminate the fraction by multiplying by \(-2\).
Therefore, the correct response is:
multiply by −2
When solving the equation −1/2(x+10)=−3, identify the operation that should be done first.(1 point)
Responses
multiply by −2
multiply by negative 2
subtract 10
subtract 10
divide by −2
divide by negative 2
add 10
7 answers
Three adult and three child movie tickets were purchased for $75. The cost of each child ticket is $3 less than the cost of an adult ticket. Identify the first step if solving this problem arithmetically, which would find the cost of one adult and one child ticket. (1 point)
Responses
Divide 75 by 6.
Divide 75 by 6.
Subtract 6 from 75.
Subtract 6 from 75.
Add 3 to 75.
Add 3 to 75.
Divide 75 by 3.
Responses
Divide 75 by 6.
Divide 75 by 6.
Subtract 6 from 75.
Subtract 6 from 75.
Add 3 to 75.
Add 3 to 75.
Divide 75 by 3.
To solve the problem, we need to set up equations based on the information given. Let's define the cost of an adult ticket as \( x \) and the cost of a child ticket as \( x - 3 \) (since the child ticket is $3 less than the adult ticket).
Next, we can express the total cost for the tickets mathematically:
\[ 3x + 3(x - 3) = 75 \]
Now, you need to simplify the equation to find the values of \( x \). The first logical step in solving this equation would be to combine the terms on the left side.
However, considering the choices provided, the best initial action aligned with the options would be to simplify the costs to find an average or total per ticket context, which would not directly match the equations formed above.
Since none of the provided options align perfectly with the specific equation formulation needed to find costs, and if we're aiming to find an average ticket cost, then:
Divide 75 by 6.
is the closest initial operation that would help since it gives a per-ticket average, although it won't yield the exact individual ticket costs immediately.
Three adult and three child movie tickets were purchased for $75. The cost of each child ticket is $3 less than the cost of an adult ticket. The first step to solving this problem algebraically is to write an equation: 3(x+x−3)=75
, where x
represents the cost of an adult ticket. Identify the next step, which would simplify the equation before solving for the variable. (1 point)
Responses
Distribute values over the variables.
Distribute values over the variables.
Divide 75 by 3.
Divide 75 by 3.
Add 3 to 75
Add 3 to 75
Combine like terms in parentheses.
, where x
represents the cost of an adult ticket. Identify the next step, which would simplify the equation before solving for the variable. (1 point)
Responses
Distribute values over the variables.
Distribute values over the variables.
Divide 75 by 3.
Divide 75 by 3.
Add 3 to 75
Add 3 to 75
Combine like terms in parentheses.
The equation you have is:
\[ 3(x + (x - 3)) = 75 \]
To simplify this equation before solving for the variable \( x \), the next step would be to distribute values over the variables.
This means you would distribute the \( 3 \) across the terms inside the parentheses:
\[ 3x + 3(x - 3) = 75 \]
So the correct response is:
Distribute values over the variables.
Three adult and three child movie tickets were purchased for $75. The cost of each child ticket is $3 less than the cost of an adult ticket. Find the price of each ticket.(1 point)
Responses
an adult ticket is $8 and a child ticket is $5
an adult ticket is $8 and a child ticket is $5
an adult ticket is $14 and a child ticket is $11
an adult ticket is $14 and a child ticket is $11
an adult ticket is $12.50 and a child ticket is $9.50
an adult ticket is $12.50 and a child ticket is $9.50
an adult ticket is $11 and a child ticket is $8
Responses
an adult ticket is $8 and a child ticket is $5
an adult ticket is $8 and a child ticket is $5
an adult ticket is $14 and a child ticket is $11
an adult ticket is $14 and a child ticket is $11
an adult ticket is $12.50 and a child ticket is $9.50
an adult ticket is $12.50 and a child ticket is $9.50
an adult ticket is $11 and a child ticket is $8
Let's solve for the cost of each adult and child ticket.
- Let \( x \) be the cost of an adult ticket.
- The cost of a child ticket will be \( x - 3 \).
Given that three adult tickets and three child tickets totaled $75, we can set up the equation:
\[ 3x + 3(x - 3) = 75 \]
Now, let's simplify this equation:
\[ 3x + 3x - 9 = 75 \] \[ 6x - 9 = 75 \]
Next, we add 9 to both sides:
\[ 6x = 84 \]
Now, divide by 6:
\[ x = 14 \]
So, the cost of an adult ticket is $14. For the child ticket:
\[ x - 3 = 14 - 3 = 11 \]
Thus, the cost of a child ticket is $11.
The prices of the tickets are:
- An adult ticket is $14.
- A child ticket is $11.
Therefore, the correct response is:
an adult ticket is $14 and a child ticket is $11.