Question

a group of adults and children go to a museum and pay $25 in admission tickets. each admission ticket costs $5, and there are 4 children in the group. the equation and solution below represent this situation. 5(x + 4)=25 step 1: 5x + 20 = 25 step 2: 5x = 5 step 3: x = 1 which of the following statements are true regarding this situation? choose either true or false next to each statement. statement step 1 is justified by the commutative property. true false step 2 is justified by the subtraction property of equality. step 3 is justified by the reflexive property of equality. the solution indicates that there is 1 adult in the group. the solution indicates that there is 1 more adult than children in the group.

Explanation:

Step1: Analyze Step 1

The step $5(x + 4)=5x + 20$ is justified by the distributive property, not the commutative property. The commutative property is for operations like $a + b=b + a$ or $a\times b = b\times a$. So the statement about Step 1 is False.

Step2: Analyze Step 2

Starting from $5x+20 = 25$, subtracting 20 from both - sides $5x+20 - 20=25 - 20$ to get $5x = 5$ is justified by the subtraction property of equality. So the statement about Step 2 is True.

Step3: Analyze Step 3

Starting from $5x = 5$, dividing both sides by 5 ($\frac{5x}{5}=\frac{5}{5}$) to get $x = 1$ is justified by the division - property of equality, not the reflexive property of equality (which is $a=a$). So the statement about Step 3 is False.

Step4: Analyze the solution meaning

If $x$ represents the number of adults, and $x = 1$, the solution indicates that there is 1 adult in the group. So this statement is True.

Step5: Analyze the comparison of adults and children

There are 4 children and 1 adult. There are 3 fewer adults than children, not 1 more adult than children. So this statement is False.

Answer:

Step 1 is justified by the commutative property. False
Step 2 is justified by the subtraction property of equality. True
Step 3 is justified by the reflexive property of equality. False
The solution indicates that there is 1 adult in the group. True
The solution indicates that there is 1 more adult than children in the group. False