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Stacia wanted concert tickets that were selling for $36 each, and then she got a $19 discount. She paid a total of $53 for the tickets. How many tickets did she buy? Identify the operations needed to solve this problem using the equation 36x −19=53

.(1 point)
Responses

addition and multiplication
addition and multiplication

subtraction and division
subtraction and division

addition and division
addition and division

subtraction and multiplication
subtraction and multiplication

5 answers

To solve the equation \( 36x - 19 = 53 \), we need to isolate the variable \( x \), which represents the number of tickets Stacia bought. Here are the steps involved:

  1. Add 19 to both sides of the equation to move the discount term to the right side: \[ 36x - 19 + 19 = 53 + 19 \] This simplifies to: \[ 36x = 72 \]

  2. Divide both sides by 36 to solve for \( x \): \[ x = \frac{72}{36} \] This simplifies to: \[ x = 2 \]

So, Stacia bought 2 tickets.

In terms of the operations used to solve the problem, we performed addition (to add 19) and division (to divide by 36).

The correct response is: addition and division.

Niel has a bucket of beads. He uses them to make 8 identical necklaces and then buys 25 beads at the store. He ends up with a total of 500 beads. How many did he start with? Identify the operations needed to solve this problem using the equation b/8 + 25 = 500
.(1 point)
Responses

addition and multiplication
addition and multiplication

subtraction and multiplication
subtraction and multiplication

addition and division
addition and division

subtraction and division

To solve for the number of beads Niel started with using the equation \( \frac{b}{8} + 25 = 500 \), where \( b \) represents the initial number of beads, we can go through the following steps:

  1. Subtract 25 from both sides of the equation to isolate the term involving \( b \): \[ \frac{b}{8} + 25 - 25 = 500 - 25 \] This simplifies to: \[ \frac{b}{8} = 475 \]

  2. Multiply both sides by 8 to solve for \( b \): \[ b = 475 \times 8 \]

By doing the calculations, we can find \( b \).

In terms of the operations required:

  • We first performed subtraction (to subtract 25).
  • Then we performed multiplication (to multiply by 8).

The correct response is: subtraction and multiplication.

A window cleaner has enough supplies to clean 21 windows per office building on a certain number of buildings. They can also clean the windows of a school with 42 windows. Altogether, there are enough supplies to clean 126 windows. How many office buildings can be washed? Identify the equation that would be used to solve this problem algebraically.(1 point)
Responses

42x−21=126
42 x minus 21 equals 126

21x−42=126
21 x minus 42 equals 126

42x+21=126
42 x plus 21 equals 126

21x+42=126

To solve the problem, let's define \( x \) as the number of office buildings the window cleaner can wash. The cleaner can clean 21 windows per office building, so the total number of windows cleaned from the office buildings would be \( 21x \).

In addition, they can clean the windows of one school, which has 42 windows.

Combining these two, we get the total amount of windows cleaned equal to the supplies available, which is 126 windows. Thus, the equation to represent this situation would be:

\[ 21x + 42 = 126 \]

This shows that the total windows cleaned from \( x \) office buildings and one school equals 126.

Therefore, the correct response is: 21x + 42 = 126.