Marie is saving money for home repairs. So far, she has saved $1,558. She needs at least $2,158 for the repairs. She plans to add $60 per week to her current savings until she can afford the repairs.
In this activity, you will algebraically model and solve an inequality based on this situation and interpret the solutions within
realistic guidelines
Part A
Question
Given the situation, which inequality models the number of additional weeks Marie needs to continue saving to afford the
home repairs?
Select the correct answer.
1,558 + 60x 22,158
60x + 1,558 5 2,158
1,558 - 60x s 2,158
2,158 - 60x 2 1,558

Inequality:  

Number of Weeks:  

Step-by-step explanation:

Given

Required

Represent this using an inequality

Represent the number of weeks as x;

This implies that, She'll save $60 * x in x weeks

Her total savings after x weeks would be

From the question, we understand that she needs at least 2158;

Mathematically, this can be represented as (greater than or equal to 2158)

Bringing the two expressions together;

Substitute 1558 for Initial Savings

Hence, the inequality that represents the situation is

Solving further for x (number of weeks)

Subtract 1558 from both sides

Divide both sides by 60

This means that she needs to save $60 for at least 10 weeks

  b.   the average rate of change of f(x) is less than the average rate of change of g(x).

step-by-step explanation:

since the length of the interval is the same in each case, we only need to compare the change in y-value to see which is greater.

so the change in y-value for function f is (6 )) = 9.

the table tells us

so the change in y-value for function g is (31 -1) = 30.

the change in y-value of f(x) on the interval is less than the change in y-value of g(x) on the same interval, so the average rate of change of f(x) is less than the average rate of change of g(x).

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