Question

Peter is saving for a down payment of $50,000 for a new home. yesterday, he created an equation that models his current savings plan to determine how long it will take him reach his goal. in his model, y represents the total amount saved and x represents the number of months since yesterday. which statement is true? a. peter used the division property of equality in step 4. b. peter used the substitution property in step 5. c. peter used the subtraction property of equality in step 5. d. peter used the associative property in step 6.

Answer 1

Without detailed steps of Peter's equation-solving process, it is impossible to determine accurately which mathematical property he used in steps 4, 5, or 6. The description of the Division, Substitution, Subtraction, and Associative properties provides general information on what each entails.

Step-by-step explanation:

The student's question pertains to the mathematical properties used in steps of solving an equation in a savings plan model. There is no specific information given about what was done in steps 4, 5, or 6, so we cannot accurately determine which property was used. However, we can explain what each property entails:

• The Division Property of Equality states that if you divide each side of an equation by the same nonzero number, the sides remain equal.
• The Substitution Property allows you to substitute one term for another that has the same value.
• The Subtraction Property of Equality allows you to subtract the same number from both sides of an equation, keeping it balanced.
• The Associative Property allows you to add or multiply regardless of how the numbers are grouped. For addition, this means (a + b) + c = a + (b + c), and for multiplication, this means (ab)c = a(bc).

Without the specific steps Peter used, we cannot accurately identify which property he implemented at each step.

Answer 2

Peter used the subtraction property of equality in step 5 of his equation to determine his savings plan.

Step-by-step explanation:

Peter created an equation to model his savings plan to determine how long it will take him to reach his goal of a $50,000 down payment for a new home. The equation is in the form y = mx + b, where y represents the total amount saved and x represents the number of months since yesterday. From the given options, the correct statement is:

c. Peter used the subtraction property of equality in step 5.

In step 5 of Peter's equation, he likely subtracted a certain amount from both sides of the equation to isolate the variable on one side. This is known as the subtraction property of equality, and it helps Peter determine how much he needs to save each month to reach his goal.