Question

example 5
solve each problem.

1. lunch account at the beginning of the quarter, nahla deposited $100 into her lunch account. if nahla spends an average of $18 per week on lunches, then $m = 100 - 18w$ represents the amount of money nahla has left in her lunch account $m$ after $w$ weeks of school.

a. use the graph to estimate to the nearest tenth the number of weeks that nahla can purchase school lunches with the money she deposited at the beginning of the quarter.
b. solve algebraically to verify your estimate. round to the nearest hundredth.

1. reading mario has a 500 - page novel which he is required to read over summer break for his upcoming language arts class.

a. if mario reads 24 pages each day, write and graph a function to represent the number of pages that mario has left to read $p$ after $d$ days.
b. estimate the zero of the function by using the graph. justify your response.
c. find the zero algebraically. interpret its meaning in the context of the situation.
example 6
solve each inequality. graph the solution set on a number line.

1. $\frac{z}{-4}geq2$
2. $3a + 7leq16$
3. $20 - 3n>7n$
4. $7f - 9>3f - 1$
5. $0.7m + 0.3mgeq2m - 4$
6. $4(5x + 7)leq13$

Explanation:

23.

Step1: Estimate from the graph

By looking at the graph, when $m = 0$ (money left is 0), we estimate the value of $w$. The line intersects the $x -$axis (weeks) at approximately $w\approx5.5$.

Step2: Solve algebraically

Set $m = 0$ in the equation $m=100 - 18w$. Then we have the equation $0 = 100-18w$. First, add $18w$ to both sides: $18w=100$. Then divide both sides by 18: $w=\frac{100}{18}=\frac{50}{9}\approx5.56$.

Step1: Write the function

The total number of pages is 500 and Mario reads 24 pages per day. So the function for the number of pages left $p$ after $d$ days is $p = 500-24d$.

Step2: Estimate the zero from the graph

To graph $p = 500 - 24d$, we can find the $y -$intercept (when $d = 0$, $p = 500$) and the $x -$intercept (the zero of the function). By graphing (a linear function with slope $- 24$ and $y -$intercept 500), we estimate the zero (where $p = 0$) to be around $d\approx20.8$. The zero represents the number of days it takes Mario to finish the book.

Step3: Find the zero algebraically

Set $p = 0$ in the equation $p = 500-24d$. Then $0=500 - 24d$. Add $24d$ to both sides: $24d=500$. Divide both sides by 24: $d=\frac{500}{24}=\frac{125}{6}\approx20.83$. In the context of the situation, it means it takes Mario about $20.83$ days to finish reading the 500 - page novel.

Step1: Solve the inequality

Start with $\frac{z}{-4}\geq2$. Multiply both sides by - 4. When multiplying an inequality by a negative number, the direction of the inequality sign changes. So $z\leq2\times(-4)$, which gives $z\leq - 8$.

Step2: Graph on a number line

Draw a number line. Mark - 8 with a closed circle (because $z$ can equal - 8) and shade to the left of - 8.

Answer:

a. Approximately $5.5$ weeks.
b. $w\approx5.56$ weeks.

24.